CH 101 Exam 1 Notes

A titanium (Ti) cube contains 2.86 x 10^23 atoms. The density of Ti equals 4.50 g/cm^3. What is the length of the cube in cm?

1.72 cm

Calculate to the correct number of significant figures. 915÷4.970 1.54×0.03060×0.69 27.5×1.82÷100.04 (2.290×106)÷(6.7×104)

1.84 0.033 0.500 34

Convert between energy units. 534 kWh to J 215 kJ to Cal 567 Cal to J 2.85×10^3 J to cal

1.92×10^9 J 51.4 cal 2.37×10^6 J 681 cal

A house has an area of 195 m^2. What is its area in: km^2 dm^2 cm^2

1.95×10^−4 km^2 1.95×10^4 dm^2 1.95×10^6 cm^2

How many 1-cm squares does it take to construct a square that is 1 m on each side?

10,000 1-cm squares

Calculate the wavelength (in nm) of the emission "line" from a hydrogen atom that corresponds to the transition of an electron from n=3 to n=1.

103 nm

Silver is composed of two naturally occurring isotopes: Ag-107 (51.839%) and Ag-109. The ratio of the masses of the two isotopes is 1.0187. What is the mass of Ag-107?

106.91 amu

deci (d)

10^-1

pico (p)

10^-12

femto (f)

10^-15

atto (a)

10^-18

centi (c)

10^-2

milli (m)

10^-3; 1mL=1cm^3

micro (upside down h)

10^-6

nano (n)

10^-9

tera (T)

10^12

peta (P)

10^15

exa (E)

10^18

kilo (k)

10^3

mega (M)

10^6

giga (G)

10^9

wave function

a mathematical function that describes the wavelike nature of the electron

wavelength

distance between adjacent crests of a wave (determines light wave's color)

speed

distance/time

spin quantum number (m sub s)

either +1/2 or -1/2, indicating the spin orientation of an electron; all electrons have the same amount of spin (fundamental property); spin up: (m sub s=+1/2) or spin down: (m sub s= -1/2)

infrared (IR) radiation

electromagnetic radiation emitted from warm objects, with wavelengths slightly larger than those of visible light

visible light

electromagnetic radiation with frequencies that can be detected by the human eye

x-rays

electromagnetic radiation with wavelengths slightly longer than gamma rays

Bohr Model

electrons travel around nucleus in circular orbits at specific fixed distances from the nucleus; no radiation is emitted by the electron orbiting the nucleus--> only when electron jumps/transitions from one orbit to another; photon's energy emitted when electron transitions is the energy difference between 2 orbits; transitions between closer orbits produce less energy of light (but higher wavelength) than farther apart orbits

raadioactivity

emission of subatomic particles or high-energy electromagnetic radiation by the unstable nuclei of certain atoms

kinetic energy

energy of motion (ball falling out of person's hand); KE= (1/2)mv^2

binding energy

energy with which an electron is bound to the metal

random error

error that has equal probability of being too high or too low (result is inconsistency which leads to inaccurate and imprecise results)

systematic error

error that tends toward being consistently either too high or too low (inaccuracy is result)

quantum mechanical model

explains the behavior of absolutely small particles such as electrons and protons

Kilowatt-hour

expresses large amounts of energy produced by flow of electricity; 1kwh= 3.60 x 10^6 J

atomic mass unit (amu)

expresses the masses of atoms and subatomic particles; defined as 1/12 the mass of a carbon atom containing 6p and 6n

Without doing any calculations, determine which of the samples contains the greatest amount of the element in moles. Which contains the greatest mass of the element? 55.0 g Cr 45.0 g Ti 60.0 g Zn

greatest number of moles: Cr, greatest mass: Zn

exact numbers

have no uncertainty and thus do not limit the number of significant figures in any calculation

violet light

high energy; shortest wavelength of visible light

microwaves

higher wavelength than IR; used for radar and in microwave ovens

interference pattern

the diffraction of light through two slits separated by a distance comparable to the wavelength of light

principal level (shell)

the group of orbitals with the same value of n

the faster an electron moves...

the higher its KE and smaller its wavelength

Which statements about subatomic particles are true? If an atom has an equal number of protons and electrons, it will be charge-neutral. Electrons are attracted to protons. Electrons are much lighter than neutrons. Protons have twice the mass of neutrons.

the last statement is false so the first 3 are true

mass of proton and nuetron

the mass of each are pretty much equal (1.67 x 10^-27 kg which is also equal to 1 amu)

threshold frequency

the minimum frequency of light required to produce the photoelectric effect; frequency at which electrons are ejected when the energy of a photon exceeds the energy with which an electron is held to the metal

atomic number (Z)

the number of protons in the nucleus of an atom; defines element and determines charge of nucleus

1s orbital

the orbital with n=1, l=0, and m sub 1=0; 1 is value of n (1 sublevel) and s specifies that l=0; high dot density near nucleus indicates higher probability density for electron there; as you move away from nucleus, the probability density decreases

probability density

the probability (per unit volume) of finding the electron at a point in space as expressed by a three-dimensional plot of the wave function squared; (ψ^2)= probability density= (probability/unit volume)

electromagnetic spectrum

the range of the wavelengths of all possible electromagnetic radiation

emission spectrum

the range of wavelengths emitted by a particular element; used to identify the element (separate the light emitted by a single element in a glass tube into its constituent wavelengths by passing through a prism); electron makes transition from higher-energy level to a lower-energy one

natural abundance

the relative percentage of a particular isotope in a naturally occurring sample with respect to other isotopes of the same element

atomic spectroscopy

the study of the electromagnetic radiation absorbed and emitted by atoms

mass number

the sum of the numbers of protons and neutrons in the nucleus of an atom

dimensional analysis

the use of units as a guide to solving problems

Classify each statement as an observation, a law, or a theory: All matter is made of tiny, indestructible particles called atoms. When iron rusts in a closed container, the mass of the container and its contents do not change. In chemical reactions, matter is neither created nor destroyed. When a match burns, heat is released.

theory observation law observation

flame tests

used to identify elements in ionic compounds in the absence of a precise analysis of a compound's spectrum

amplitude

vertical height of a crest (or depth of a trough) of a wave; measure of wave intensity (the higher the amplitude, the higher the intensity)

wave view of light (electromagnetic radiation) equation

wavelength= c/v

wave view of matter (diffraction of e-) equation

wavelength= h/mv

deBrogile relation

wavelength=h/mv; wavelength of electron of mass (m) moving at velocity (v); h is Planck's constant= 6.626x10^-34 J*s; mv= momentum

destructive interference

waves align so that one crest overlaps with a trough from another wave (cancellation)

constructive interference

waves align with overlapping crests (increase in amplitude)

law of mulitple proportions

when two elements (A and B) form two diff compounds, the masses of element B that combine with 1g of element A can be expressed as a ratio of small whole numbers

phase

with regard to waves and orbitals, the sign of the amplitude of the wave, which can be positive or negative

equation for emission spectra of hydrogen atom

ΔE= -2.18f x 10^-18 J(1/n^2f - 1/n^2i) use negative when asked energy of electron when it falls from n to n but use absolute value of equation when asked energy of a photon emitted from the electron transfer

difference in energy between two orbital levels:

ΔE=Efinal−Einitial

Heisenberg's uncertainty principle

ΔX x mΔv >= h/4pi ; Δx= uncertainty in position; Δv uncertainty in velocity

An electron has an uncertainty in its position of 552 pm. What is the uncertainty in its velocity? (Hint: Δx=552×10^−12 m; use Heisenberg's uncertainty principle to calculate Δv.)

Δν=1.04×10^5 m/s

Law of Conservation of Energy

Energy cannot be created or destroyed only converted from one from to another

particle view of light (photoelectric effect) equation

Energy= hv ; massless particles called photons

mole (mol)

amount of material containing 6.022x10^23 atoms/particles (Avogadro's number)

energy

the capacity to do work

formula for atomic mass using various isotopes

(% (in decimal form) natural abundance of 1)x(mass of 1) + (% (decimal) of 2)x(mass of 2)

ultraviolet (UV) radiation

(between x-rays and visible light); electromagnetic radiation with slightly smaller wavelengths than visible light

List these types of electromagnetic radiation in order of (i) increasing wavelength and (ii) increasing energy per photon: a. radio waves b. microwaves c. infrared radiation d. ultraviolet radiation

(i): d,c,b,a (ii): a,b,c,d

electromagnetic radiation

(light); form of energy embodied in oscillating electric and magnetic fields

sigfig rules in calculations:

+/- : result has same number decimal places as quantity with fewest decimal places x/division: result has same number sigfigs as factor with fewest sigfigs

fundamental charge of electron

-1.60 x !06-19; magnitude of electron's charge is important because it determines how strongly an atom holds its electrons

exact numbers originate from:

-accurate counting of discrete objects (14 pencils= 14.00000...) -defined quantities/"by definition" (100 cm in 1m) -integral numbers part of an equation (radius= diameter/2 --> 2 is exact #)

John Dalton's Atomic Theory

-each element is composed of tiny, indestructible particles called atoms -all atoms of a given element have the same mass and other properties that distinguish them from the atoms of other elements -atoms combine in simple, whole-number ratios to form compounds -atoms of one element cannot change into atoms of another element (in chemical rxns atoms only change the way they are bound together with other atoms)

Rutherford's Nuclear Theory

-most of the atom's mass and all of its positive charge are contained in a small core called a nucleus (protons and neutrons) -most of the volume of the atom is empty space, throughout which tiny, negatively charged electrons are dispersed -there are as many negatively charged electrons outside the nucleus as there are positively charged particles (named protons) within the nucleus, so that the atom is electrically neutral

sigfig rules

-nonzero digits are significant -interior zeros (zeros btwn 2 nonzero digits) are significant -zeros to left of first nonzero digit are NOT significant (0.0032 --> 2 sigfigs) -trailing zeros after decimal point are significant (45.000; 3.5600) -trailing zeros before decimal point and after nonzero number are significant (140.00; 2500.55)

matter is particulate in 3 categories:

-of samples before and after a rxn -of different samples of the same compound -of different compounds composed of the same elements

Convert each temperature. 32 °F to °C (temperature at which water freezes) 77 K to °F (temperature of liquid nitrogen) −109 °F to °C (temperature of dry ice) 98.6 °F to K (body temperature)

0 °C −321° −78.3° 310.2 K

In a technique used for surface analysis called auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons—called auger electrons—from the metal surface. The kinetic energy of the auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in auger electrons with a kinetic energy of approximately 506 eV. What is the de Broglie wavelength of one of these electrons? [KE=12mv2; 1 electron volt (eV)=1.602×10−19 J]

0.0547 nm

What is the amount, in moles, of each elemental sample? 11.8 g Ar 3.55 g Zn 26.1 g Ta 0.211 g Li

0.295 mol Ar 0.0543 mol Zn 0.144 mol Ta 0.0304 mol Li

The ratio of oxygen to nitrogen by mass in NO sub 2 is 2.29. The ratio of fluorine to nitrogen by mass in NF sub 3 is 4.07. Find the ratio of oxygen to fluorine by mass in OF sub 2.

0.423

Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 175-L tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of 1.15 g/L at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all 175 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured 10.00 m×10.00 m×2.50 m. What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?

0.492

A length of #8 copper wire (radius=1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω/km). What is the overall resistance of the wire? (Hint: Begin by using the mass and the density of copper to determine the volume of the wire and then use V=π⋅r2⋅l to determine the length of the wire.)

0.661 Ω

The average U.S. farm occupies 435 acres. How many square miles is this? (1 acre=43,560 ft2, 1 mile=5280 ft)

0.680 mi^2

An acetaminophen suspension for infants contains 80 mg/0.80 mL suspension. The recommended dose is 15 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 14 lb? (Assume two significant figures.)

0.95 mL

Round each number to four significant figures. 156.852 156.842 156.849 156.899

156.9 156.8 156.8 156.9

Calculate the number of atoms in each sample. 5.18 g P 2.26 g Hg 1.87 g Bi 0.082 g Sr

1.01×10^23 atoms 6.78×10^21 atoms 5.39×10^21 atoms 5.6×10^20 atoms

A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?

1.03 x 10^16 photons

Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?

1.1 x 10^-34 m; wavelength of baseball is negligible with respect to its size

The distance between the earth and sun is 1.49 x 10^11 m. How many copper (Cu) atoms would be needed to bridge this distance if they were lined up one after another in an "atomic row". The diameter of a single Cu atom in 140. pm.

1.1 x 10^21 Cu atoms

Use the prefix multipliers to express each measurement without any exponents. 1.2×10^−9 m 22×10^−15 s 1.5×10^9 g 3.5×10^6 L

1.2 nm 22 fs 1.5 Gg 3.5 ML

Glycerol is a syrupy liquid used in cosmetics and soaps. A 3.25-L sample of pure glycerol has a mass of 4.10×10^3 g. What is the density of glycerol in g/cm3?

1.26 g/cm^3

A 7.83-g sample of HCN contains 0.290 g of H and 4.06 g of N. Find the mass of carbon in a sample of HCN with a mass of 3.37 g.

1.50 g

Convert 15.0 L to each unit. mL cm^3 gal qt

1.50×10^3 mL 1.50×10^3 cm^3 3.96 gal 15.9 qt

The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s−1 and the highest frequency of a piccolo is 1.5×10^4 s^−1 Determine the difference in wavelength between these two sounds.

11m

An element has two naturally occurring isotopes. Isotope 1 has a mass of 120.9038 amu and a relative abundance of 57.4%, and isotope 2 has a mass of 122.9042 amu. Find the atomic mass of this element and identify it.

121.8 amu, Sb

Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. n=2→n=1 n=3→n=1 n=4→n=2 n=5→n=2

122 nm, UV 103 nm, UV 486 nm, visible 434 nm, visible

Determine the approximate percent increase in waist size that occurs when a 155-lb person gains 40.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is 4.0 ft tall. The average density of a human is about 1.0 g/cm^3, and the density of fat is 0.918 g/cm^3.

13%

A hydrogen-filled balloon is ignited and 1.50 g of hydrogen reacts with 12.0 g of oxygen. How many grams of water vapor form? (Assume that water vapor is the only product.)

13.5 g

A ruler used to measure a penny has markings every 1 mm. Which measurement for the size of the penny is correctly reported for this ruler? 19.05 mm 19 mm 19.1 mm

19.1 mm (the final digit is estimated)

molecules

2 or more atoms joined chemically in a specific geometrical arrangement

pure substance

2 types: element or compound; made of only one type of particle and composition does not vary from one sample to another; can be individual atoms or atoms grouped together (helium, water, table salt --> sodium chloride)

mixture

2 types: heterogeneous and homogeneous; made of 2 or more different types of atoms or molecules that combine into variable proportions (sweet tea --> water molecules and sugar molecules)

How many silver atoms are there in 3.78 g of silver?

2.11 x 10^22 atoms

The U.S. Environmental Protection Agency (EPA) sets limits on healthful levels of air pollutants. The maximum level that the EPA considers safe for lead air pollution is 1.5 μg/m^3. If your lungs were filled with air containing this level of lead, how many lead atoms would be in your lungs? (Assume a total lung volume of 5.50 L.)

2.4 x 10^13 atoms

The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02×10^23 hydrogen atoms. The diameter of a ping pong ball is 4.0 cm. Find the length in kilometers of a row of 6.02×10^23 ping pong balls.

2.4 x 10^19 km

How many carbon atoms are there in a diamond (pure carbon) with a mass of 52 mg?

2.6 x 10^21 atoms

Perform each unit conversion. 27.8 L to cm^3 1898 mg to kg 198 km to cm

2.78×10^4 cm^3 1.898×10^−3 kg 1.98×10^7 cm

speed of light

2.9979 x 10^8 m/s; waves of the electric and magnetic fields move at this constant speed in a vacuum

A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/mL, what mass of fuel has the airplane taken on?

201. x 10^3 g

The density of titanium is 4.51 g/cm^3. What is the volume (in cubic inches) of 3.5 lb of titanium?

21 in^3

The mass ratio of sodium to fluorine in sodium fluoride is 1.21:1. A sample of sodium fluoride produces 28.8 g of sodium upon decomposition. How much fluorine (in grams) is formed?

23.8 g

Naturally occurring magnesium has an atomic mass of 24.312 and consists of three isotopes. The major isotope is ^24Mg, natural abundance 78.99%, relative atomic mass 23.98504. The next most abundant isotope is ^26Mg, relative atomic mass 25.98259. The third most abundant isotope is ^25Mg whose natural abundance is in the ratio of 0.9083 to that of ^26Mg. Find the relative atomic mass of ^25Mg.

25.06 g/mol

Express the quantity 254,998 m in each unit. km Mm mm cm

254.998 km 2.54998×10^−1 Mm 254998×10^3 mm 254998×10^2 cm

Determine the number of protons and the number of electrons in each ion. Ni^2+ S^2- Br^− Cr^3+

28p and 26e− 16p and 18e− 35p and 36e− 24p and 21e−

how to find number of orbitals in a sublevel:

2l+1; the sublevel l=0 (s) has 1 orbital; the p sublevel (l=1) has 3 orbitals; the d sublevel (l=2) has 5 orbitals

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 2p→1s or 3p→1s?

2p→1s

Which electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?

2s

How many significant figures are in each number? 0.000312 m 312,000 s 3.12×10^5 km 13,127 s 2000

3 ambiguous, without more information assume three significant figures 3 5 ambiguous, without more information assume one significant figure

Calculate the wavelength (in A*; 1 A*= 10^-10 m) of an electron moving at 2.42 x 10^6 m/s. Calculate the wavelength (in m) 50.0 g golfball traveling at 200 mph.

3.01 A*; 1.48 x 10^-34 m

A backyard swimming pool holds 185 cu yd (yd^3) of water. What is the mass of the water in pounds?

3.11 x 10^5 lb

Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths 632.8 nm (wavelength of red light from helium-neon laser) 503 nm (wavelength of maximum solar radiation) 0.052 nm (wavelength contained in medical X-rays)

3.14×10^−19 J 3.95×10^−19 J 3.8×106−15 J

Calculate the average mass, in grams, of one platinum atom.

3.239 x 10^-22 g

The Toyota Prius, a hybrid electric vehicle, has a U.S. Environmental Protection Agency (EPA) gas mileage rating of 52 mi/gal in the city. How many kilometers can the Prius travel on 15 L of gasoline?

3.3 x 10^2 km

How many sulfur atoms are there in 5.52 mol of sulfur?

3.32 x 10^24 atoms

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

3.6 x 10^6 m/s

A cube has an edge length of 7 cm. If it is divided up into 1-cm cubes, how many 1-cm cubes are there?

343 cubes

Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A typical carbon-carbon bond requires 348 kJ/mol to break. What is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?

344 nm

Calculate the mass, in grams, of each sample. 1.1×10^23 gold atoms 2.82×10^22 helium atoms 1.8×10^23 lead atoms 7.9×10^21 uranium atoms

36 g 0.187 g 62 g 3.1 g

Calculate to the correct number of significant figures. (24.6681×2.38)+332.58 (85.3−21.489)÷0.0059 (512÷986.7)+5.44 [(28.7×105)÷48.533]+144.99

391.3 1.1×10^4 5.96 5.93×10^4

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n−1). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? n=1 n=2 n=3

4 9 16

A European automobile has a gas mileage of 17 km/L. What is the car's gas mileage in miles per gallon?

4.0 x 10^1 mi/gal

A household receives a $145 electricity bill. The cost of electricity is $0.120/kWh. How much energy, in joules, did the household use?

4.35 x 10^9 J

Use scientific notation to express each quantity with only the base units (no prefix multipliers). 4.5 ns 18 fs 128 pm 35 μm

4.5×10^−9s 1.8×10^−14s 1.28×10^−10m 3.5×10^−5m

Calculate the frequency of each wavelength of electromagnetic radiation: 632.8 nm (wavelength of red light from helium-neon laser) 503 nm (wavelength of maximum solar radiation) 0.052 nm (wavelength contained in medical X-rays)

4.74×10^14 Hz 5.96×10^14 Hz 5.8×10^18 Hz

A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? The volume of a sphere is (4/3) πr^3, and the density of copper is 8.96 g/cm^3

4.76 x 10^24 atoms

The binding energy of electrons in a metal is 193 kJ/mol. Find the threshold frequency of the metal.

4.84×10^14 s^−1

A bluray DVD player used a laser that emits 405 nm light. What is the energy (in J) of a single photon at 405 nm?

4.90 x 10^-19 J

Calculate to the correct number of significant figures. 43.7−2.341 17.6+2.838+2.3+110.77 19.6+58.33−4.974 5.99−5.572

41.4 133.5 73.0 0.42

Ethylene glycol (antifreeze) has a density of 1.11 g/cm^3. What is the mass in g of 417 mL of this liquid? What is the volume in L of 4.1 kg of this liquid?

463 g 3.7 L

Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 g of sodium per day. A particular snack mix contains 1.25 g of salt per 100 g of the mix. What mass of the snack mix can an adult consume and not exceed the FDA limit?

488 g

How many electrons, protons, and neutrons in the ^114Cd^2+ isotope?

48p 66n 46e-

The distance from the sun to Earth is 1.496×10^8 km. How long does it take light to travel from the sun to Earth?

499 s

A runner wants to run 10.0 km. She knows that her running pace is 7.5 miles per hour. How many minutes must she run?

5.0 x 10^1 min

What is the de Broglie wavelength of an electron traveling at 1.35×10^5 m/s ?

5.39 nm

How many protons and neutrons are there in the 146/57 La isotope?

57p 89n

The binding energy (photoelectric effect) of Cesium (Cs) metal is 3.42 x 10^-19 J. Calculate the longest possible wavelength of light (in nm) that will eject an electron from the metal.

581 nm

A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)? For comparison, the sun is about 150 million km from Earth and the nearest star, Proxima Centauri, is about 40 trillion km from Earth.

6.0 x 10^17 km

An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons will travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W=1 J/s) Hint: Use the formula for the area of a circle (A=πr2)to find the cross-sectional area of the beam and of the pinhole and determine what fraction of the power gets through the pinhole.

6.4 x 10^17 photons/s

The iodine molecule can be photo dissociated (broken apart with light) into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A glass tube contains 1.80×10^17 iodine molecules. What minimum amount of light energy must be absorbed by the iodine in the tube to dissociate 15.0% of the molecules?

6.78 x 10^-3 J

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0×10^−13 cm. The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus? (Hint: Start by calculating the volume of the nucleus and the volume of the atom.)

6.8 x 10^-15

Perform each unit conversion. 154 cm to in 3.14 kg to g 3.5 L to qt 109 mm to in

60.6 in 3.14×10^3 g 3.7 qt 4.29 in

A 7.36-g sample of copper is contaminated with an additional 0.51 g of zinc. Suppose an atomic mass measurement is performed on this sample. What would be the apparent measured atomic mass?

63.67 g/mol

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29×10^20 photons. What is the wavelength of the laser?

632 nm

Calculate the wavelength (in nm) of light emitted by a bar code scanner that has a frequency of 4.62 x 10^14 s^-1

647 nm

Gallium (Ga) has two isotopes: Ga-69 and Ga-71. The atomic mass of Ga-69 is 68.93 amu and represents 60.11% of the Ga found in nature. The atomic mass of the Ga-71 isotope is 70.92 amu and represents 39.89% of the Ga found in nature. What is the value of the mass of Ga reported in the Periodic Table?

69.72 amu

The amount of carbon-14 in ancient artifacts and fossils is often used to establish their age. Determine the number of protons and the number of neutrons in a carbon-14 isotope and write its symbol in the form A/Z X

6p 8n; 14/6 C

The density of elemental mercury (Hg) is 13.5 g/mL. How many Hg atoms are in 1.85 mL of Hg?

7.5 x 10^22 atoms Hg

A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm^3?

7.6 g/cm^3

A 67.2-g sample of a gold and palladium alloy contains 2.49×10^23 atoms. What is the composition (by mass) of the alloy?

75.0% gold

Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) infrared radiation (1500 nm) visible light (500 nm) ultraviolet radiation (150 nm)

79.8 kJ/mol 239 kJ/mol 798 kJ/mol

Determine the number of protons and the number of neutrons in each isotope. 14/7 N 23/11 Na 222/86 Rn 208/82 Pb

7p 7n 11p 12n 86p 136n 82p 126n

Polluted air can have carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide does the average person inhale in an 8-hour period in this level of carbon monoxide pollution? Assume that the carbon monoxide has a density of 1.2 g/L. (Hint: 15.0 ppm CO means 15.0 L CO per 106106 L air.)

9 x 10^1 mg CO

mass of electron

9.11 x 10^-31 kg

Suppose that a person eats 2387 Calories per day. Convert this amount of energy into each unit. J kJ kWh

9.987×10^6 J 9.987×10^3 kJ 2.78 kWh

Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?

91.2 nm

radial distribution function

A mathematical function (corresponding to a specific orbital) that represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus; total radial probability (at a given r)= (probability/unit volume) x volume of shell at r; shape of radial distribution function is result of multiplying together two functions with opposite trends in r: the probability density function (ψ^2), which is the probability per unit volume, has a maximum at the nucleus and decreases with increasing r; the volume of the thin shell, which is zero at the nucleus, increases with increasing r

mass

A measure of the amount of matter in an object

work

A result of a force moving an object a certain distance (pushing box across floor or pedal bike down street)

Write isotopic symbols in the form X-A (e.g., C-13) for each isotope. the silver isotope with 60 neutrons the silver isotope with 62 neutrons the uranium isotope with 146 neutrons the hydrogen isotope with 1 neutron

Ag-107 Ag-109 U-238 H-2

Bromine has two naturally occurring isotopes (Br-79 and Br-81) and an atomic mass of 79.904 amu. The mass of Br-81 is 80.9163 amu, and its natural abundance is 49.31%. Calculate the mass and natural abundance of Br-79.

Br-79 78.92 amu 50.96%

equation of energy of n (principal level)

En= -2.18 x 10^-18 J(1/n^2) describes the energy of an electron of n in an orbital En=1 = -2.18 x 10^-18 J

Albert Einstein and the photoelectric effect

E=hv; h=Planck's constant= 6.626x10^-34 J*s; light energy must come in packets; amount of energy (E) in a light packet depends on its frequency (v); E=hc/wavelength because v=c/wavelength; Energy of photon is directly proportional to frequency and inversely proportional to wavelength

gamma rays

Electromagnetic waves with the shortest wavelengths and highest frequencies; high energy

boiling, freezing, and absolute zero points of F, C, and K:

F: boils at 212 deg, freezes at 32 deg, absolute zero at -459 deg C: boils at 100 deg, freezes at 0 deg, absolute zero at -273 deg K: boils at 373, freezes at 273, absolute zero at 0

Two different compounds containing osmium and oxygen have the following masses of oxygen per gram of osmium: 0.168 and 0.3369 g. Show that these amounts are consistent with the law of multiple proportions.

For the law of multiple proportions to hold, the ratio of the masses of O combining with 1 g of Os in the compound should be a small whole number. 0.3369/0.168=2.00

How and by whom was the electron discovered? What basic properties of the electron were reported with its discovery?

J.J. Thomson's experiments with cathode ray tubes showed that all atoms contain tiny negatively charged subatomic particles or electrons. Thomson proposed the plum pudding model of the atom, which had negatively-charged electrons embedded within a positively-charged "soup."

Sulfur and oxygen form both sulfur dioxide and sulfur trioxide. When samples of these are decomposed, the sulfur dioxide produces 3.49 g oxygen and 3.50 g sulfur, while the sulfur trioxide produces 6.75 g oxygen and 4.50 g sulfur. Calculate the mass of oxygen per gram of sulfur for each sample and show that these results are consistent with the law of multiple proportions.

Sample 1: 1.00 g O2/1.00 g S; Sample 2: 1.50 g O2/1.00 g S Sample 2/Sample 1=1.50/1.00=1.50 3 O atoms/2 O atoms=1.5

total energy

TE=KE+PE; does not change

Joule (J)

The SI unit of energy, 1kg*m*m/s/s. A related unit is the calorie: 4.184J = 1 cal.

Diffraction

The bending of a wave as it moves around an obstacle or passes through a narrow opening

The atomic mass of fluorine is 18.998 amu, and its mass spectrum shows a large peak at this mass. The atomic mass of chlorine is 35.45 amu, yet the mass spectrum of chlorine does not show a peak at this mass. Explain the difference.

The fluorine-19 isotope must have a large percent abundance, which would make fluorine produce a large peak at this mass. Chlorine has two isotopes (Cl-35 and Cl-37). The atomic mass is simply the weighted average of these two, which means that there is no chlorine isotope with a mass of 35.45 amu.

Two samples of carbon tetrachloride are decomposed into their constituent elements. One sample produces 38.9 g of carbon and 448 g of chlorine, and the other sample produces 14.8 g of carbon and 134 g of chlorine. Are these results consistent with the law of definite proportions? Show why or why not.

These results are not consistent with the law of definite proportions because sample 1 is composed of 11.5 parts Cl to 1 part C and sample 2 is composed of 9.05 parts Cl to 1 part C. The law of definite proportions states that a given compound always contains exactly the same proportion of elements by mass.

volume of sphere

V=4/3πr³

volume of cylinder

V=πr²h

Carbon-12 contains 6 protons and 6 neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers), and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom. What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)

Vn=8.2×10^−8 pm^3, Va=1.4×10^6 pm^3, 5.9×10^−12 %

deterministic

a characteristic of the classical laws of motion, which imply that present circumstances determine future events; according to classical physics particles move in a path determined by the particle's velocity, position, and forces acting on it

Nuclei with the same number of neutrons but different mass numbers are called isotones. Write the symbols of four isotones of ^236Th

^237Pa, ^238U, ^239Np, ^240Pu, ^235Ac, ^234Ra

chemical symbol

a one- or two-letter abbreviation for an element that is listed directly below its atomic number on the periodic table

node

a point where the wave function, and therefore the probability density and radial distribution function, all go through zero; probability of finding an electron at a node is zero

orbital

a probability distribution map, based on the quantum mechanical model of the atom, used to describe the likely position of an electron in an atom; also an allowed energy state for an electron

extensive property

a property that depends on the amount of matter in a sample (ex: mass)

intensive property

a property that depends on the type of matter in a sample, not the amount of matter (ex: density)

magnetic field

a region of space where a magnetic particle experiences a force (think of space around a magnet)

electric field

a region of space where an electrically charged particle experiences a force (proton has electric field around ot so bringing another charged particle into the field will cause the particle to experience a force)

cathode ray

a stream of electrons produced when a high electrical voltage is applied between two electrodes within a partially evacuated tube; the particles carried a negative electrical charge which results in attractive and repulsive forces (electrostatic forces) btwn the particles; electric field= area around charged particle

thermal energy

a type of kinetic energy associated with the temperature of an object, arising from the motion of individual atoms or molecules in the object (ball hitting ground --> the KE of ball is transferred to atoms/molecules in the ground which raises the temp of the ground)

endothermic

absorbs heat from surroundings (system gains thermal energy --> change in energy is positive)

law of definite proportions/ law of constant composition

all samples of a given compound, regardless of their source or how they were prepared, have the same proportions of their constituent elements (elements composing a compound occur in definite proportions in all samples of the compound

Schrödinger equation

an equation that describes how the quantum state of a physical system changes with time; Hψ = Eψ; H stands for the Hamiltonian operator (a set of mathematical operations that represents the total energy (kinetic and potential) of the electron within the atom); E is the actual energy of the electron; ψ is the wave function; the equation yields many possible wave functions; allows us to calculate the probability of finding an electron with a particular amount of energy at a particular location in the atom; only exact solutions for hydrogen atom; the solutions are the four quantum numbers (n, l, m sub l, m sub s)

mass spectrometry

an experimental method of determining the precise mass and relative abundance of isotopes in a given sample using an instrument called a mass spectrometer

angular momentum quantum number (l)

an integer that determines the shape of an orbital; for a given value of n, l can be any integer (including 0) up to (n−1); for example, if n=1, then the only possible value of l is 0; if n=2, the possible values of l are 0 and 1;

magnetic quantum number (m sub l)

an integer that specifies the orientation of an orbital; the possible values of m sub l are the integer values (including zero) ranging from −l to +l. For example, if l=0, then the only possible value of m sub l is 0; if l=1, the possible values of m sub l are -1, 0, and +1; if l=2, the possible values of m sub l are −2, −1, 0, +1, +2, and so on

principal quantum number (n)

an integer that specifies the overall size and energy of an orbital. The higher the quantum number n, the greater the average distance between the electron and the nucleus and the higher its energy; n=1,2,3....; For the hydrogen atom, the energy of an electron in an orbital with quantum number n is given by: E sub n= -2.18x10^-18 J (1/n^2); orbitals with higher values of n have greater energies (less negative); as n increases, the distance between energy levels becomes smaller

matter

anything that occupies space and has mass; particulate (composed of particles)--> structure of these particles determines the properties of matter

ion

atom or molecule with net charge caused by loss or gain of electrons (if atom loses electron then it has more protons so atom will no longer be electrically neutral and will instead have a positive charge and vice versa)

isotopes

atoms with the same number of protons but different numbers of neutrons (and therefore have different masses)

gas

atoms/molecules have lots of space btwn them and are free to move (no definite shape or volume); conforms to container; compressible

liquid

atoms/molecules packed but are free to move (fixed volume but not fixed shape)

solid

atoms/molecules packed close to one another in fixed locations with definite volume

atomic mass/weight

average mass in amu of the atoms of a particular element based on the relative abundance of the various isotopes; numerically equivalent to the mass in grams of one mole of the element

scientific law

brief statement or equation that summarizes past observations and predicts future ones (series of similar observations)

Which set of quantum numbers cannot occur together to specify an orbital? a. n=2,l=1,ml=−1 b. n=3,l=2,ml=0 c. n=3,l=3,ml=2 d. n=4,l=3,ml=0

c

derived unit

combination of base units (speed= m/s; velocity=km/s; density= g/cm^3; volume= m^3 or cm^3 or mm^3)

Which statements are consistent with Rutherford's nuclear theory as it was originally stated? Why? The volume of an atom is mostly empty space. The nucleus of an atom is small compared to the size of the atom. Neutral lithium atoms contain more neutrons than protons. Neutral lithium atoms contain more protons than electrons.

consistent: Rutherford's nuclear model states that the atom is largely empty space. consistent: Rutherford's nuclear model states that most of the atom's mass is concentrated in a tiny region called the nucleus. not consistent not consistent

absorption spectrum

consists of dark lines on a bright background; plot of absorption of light of a sample of matter as a function of wavelength; measured by passing white light through a sample and observing what wavelengths are missing due to absorption by the sample; electron makes transition from lower to higher energy level

white light

contains spectrum of wavelengths/colors (red, orange, yellow, green, blue, indigo, violet)

experiment

controlled procedure to generate observations that may support a hypothesis or prove it wrong

Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous. sweat carbon dioxide aluminum vegetable soup

homogeneous mixture pure substance, compound pure substance, element heterogeneous mixture

precision

how close a series of measurements are to one another or how reproducible they are (consistency)

law of conservation of mass

in a chemical rxn, matter is neither created nor destroyed (total mass of substances involved in the chemical rxn does not change)

reliability of measurement depends on...

instrument used to make measurement

hypothesis

interpretation or explanation of an observation; a good one is falsifiable--> predictions can be confirmed or refuted

What are the possible values of l for each given value of n? 1 2 3 4

l=0 l=0,1 l=0,1,2 l=0,1,2,3

Identify each statement as being most like an observation, a law, or a theory. All coastal areas experience two high tides and two low tides each day. The tides in Earth's oceans are caused mainly by the gravitational attraction of the moon. Yesterday, high tide in San Francisco Bay occurred at 2:43 a.m. and 3:07 p.m. Tides are higher at the full moon and new moon than at other times of the month.

law theory observation law

radiowaves

longest wavelength and lowest energy and lowest frequency

red light

low energy; longest wavelength of visible light

molar mass

mass (g) of 1 mol of atoms of an element (equivalent to atomic mass of element (amu))

A solid gold cylinder sits on a weight-sensitive alarm. A thief uses a can of sand to replace the solid gold cylinder. The can of sand and the gold cylinder have exactly the same dimensions (length=22 cm and radius=3.8 cm) Calculate the mass of the gold cylinder and can of sand (ignore the mass of the can itself). (density of gold=19.3 g/cm^3,density of sand=3.00 g/cm^3) Did the thief set off the alarm? Explain.

mass of can of gold=1.9×10^4 g; mass of can of sand=3.0×10^3 g Yes, the thief sets off the trap because the can of sand is lighter than the gold cylinder.

density (d)

mass/volume; decreases as temp increases

weight

measure of gravitational pull on an object's matter

SI units of: length, mass, time, temp.

meter, kilogram, second, Kelvin

heterogeneous

mixture; composition varies from one region to another (water and sand: 2 types particles that separate into 2 distinct regions)

why are atoms depicted as spherical?

most atoms contain many electrons occupying a number of different orbitals

An electron in a hydrogen atom is excited with electrical energy to an excited state with n=2. The atom then emits a photon. What is the value of n for the electron following the emission?

n=1

An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?

n=2

An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.

n=4 --> n=3, n=5 --> n=3, n=6 --> n=3, respectively

how to find number of orbital in a principal level:

n^2; n=1 level has 1 orbital; n=2 level has 4 orbitals; n=3 level has 9 orbitals

anion

negatively charged ion (Li-)

electron

negatively charged low-mass particle found outside nucleus of all atoms; occupies most of atom's volume but contributes to almost none of its mass

A new penny has a mass of 2.49 g and a volume of 0.349 cm^3 is the penny made of pure copper? Explain.

no because the density of the penny is less than that of pure copper; density of pure Cu= 8.93 g/cm^3

neutrons

not charged; neutral particles within nucleus (similar mass to proton)

Which statements are consistent with Dalton's atomic theory as it was originally stated? Why? Sulfur and oxygen atoms have the same mass. All cobalt atoms are identical. Potassium and chlorine atoms combine in a 1:1 ratio to form potassium chloride. Lead atoms can be converted into gold.

not consistent consistent: Dalton's atomic theory states that the atoms of a given element are identical. consistent: Dalton's atomic theory states that atoms combine in simple whole-number ratios to form compounds. not consistent

Which numbers are exact (and therefore have an unlimited number of significant figures)? π=3.14 12 inches=1 foot EPA gas mileage rating of 26 miles per gallon 1 gross=144

not exact exact not exact exact

frequency (v)

number of cycles or complete wavelengths that pass through a stationary point in 1 second (Hz= cycles/s= s^-1); directly proportional to speed at which wave is travelling and inversely proportional to wavelength; directly proportional to energy

quantum number

one of four interrelated numbers that determine the shape and energy of orbitals, as specified by a solution of the Schrodinger equation

chemical rxn

one or more substances are converted into one or more different substances; mass of reactants (sodium and chlorine)= mass of product (sodium chloride); particles in the matter rearrange during a chemical rxn but the number of particles is conserved because particles are indestructible by chemical means

isotope symbolization

or X-A

sublevel (subshell)

orbitals in the same principal level with the same value of n and l

photoelectric effect

particle nature of light; observation that many metals emit electrons when light falls upon the metal

trajectory

particles move in this path; determined by the particle's velocity (speed and direction of travel), its position, and the forces acting on it

cation

positively charged ion (Li+)

Interdeterminacy

present circumstances do not necessarily determine future events in the quantum-mechanical realm (electron); we cannot know both the position and velocity of an electron so we cannot predict the path it will follow--> the best we can do is describe the probability of an electron will be found in a particular region using statistical functions (probability distribution map)

2p orbital

principal level n=2; l=1; contains 3 p orbitals: m sub l= -1,0,+1; not spherically symmetrical like s orbitals--> instead have 2 lobes of electron density on either side of the nucleus and a node located at the nucleus; the three p orbitals differ in orientation and are perpendicular to each other

3d orbital

principal level n=3; l=2; contains 5 d orbitals: m sub l= -2,-1,0,1,2; four of the orbitals have cloverleaf shape with four lobes of electron density around nucleus and two perpendicular nodal planes (plane where electron probability density is zero

4f orbital

principal level n=4; l=3; contains seven f orbitals: m sub l= -3,-2,-1,0,1,2,3

complementary properties

properties that exclude one another, that is , the more you know about one, the less you know about the other; for example, the wave nature and particle nature of the electron are complementary; our inability to observe an electron simultaneously as both a particle and wave means that we cannot simultaneously measure its position (based on particle nature) and velocity (based on wave nature) with infinite precision; electron is either particle or wave but never both at once; velocity is directly related to energy (KE=1/2 mv^2) so position and energy are also complementary properties

theory

proposed explanation for observations and laws based on well-tested hypotheses; model of the way nature works and predicts behavior beyond observations and laws on which it was based

element

pure substance; cannot be chemically broken down into simpler substances

compound

pure substance; composed of 2 or more elements in fixed, definite proportions (water: H2O)

photon

quantum/packet of light; smallest possible packet of electromagnetic radiation wit an energy equal to hv; number of photons=Epulse/Ephoton

photon threshold frequency

reached when Ephoton= binding energy (for an electron bound to metal); as the frequency of light increases over the threshold frequency, excess E of the photon (beyond what is needed to dislodge electron) transfers to electrons

accuracy

refers to how close the measured value is to the actual value

exothermic

releases heat to surroundings (system loses thermal energy --> change in energy is negative)

homogeneous

same composition throughout; 2 types particles that thoroughly mix (sweet tea)

What is the significance of the number of digits reported in a measured quantity?

scientists report measured quantities so digits reflect measurement certainty; more digits=more certainty

Why does a red shirt appear red?

shirt reflects red light while absorbing the other colors (we see the reflected light)

atom

simplest chemical building block; basic particles that compose ordinary matter

sunstance

specific instance of matter (air, water, sand)

potential energy

stored energy that results from the position or shape or composition of an object (ball in person's hand); high PE= unstable; when ball falls --> less PE= stable; difference in PE allows work to occur

interference

superposition of 2 or more waves overlapping in space, resulting in either an increase in amplitude (constructive) or decrease in amplitude (destructive)

The coldest temperature ever measured in the United States is −80 °F on January 23, 1971, in Prospect Creek, Alaska. Convert that temperature to °C and K. (Assume that −80 °F is accurate to two significant figures.)

−62.2 °C, 210.9 K