Chem 101 chapter 6 general chemistry

What is the energy of the electron in a helium ion with a charge of +1 in an orbit with a value of n=4? Use k=2.179×10−18J.

-5.45 x 10^-19J $-5.45\times10^{-19}\text{ J}$−5.45×10−19 J​ First, recall that the energy of the electron in a single-electron atom or ion is described by the equation: E=−kZ2n2 where k is the Rydberg constant (2.179×10−18 J), Z is the atomic number of the atom, and n is the energy level occupied by the electron. Substitute in the known values and solve: EE=−(2.179×10−18)(2)2(4)2=−5.45×10−19 J Notice that values for n (energy level occupied by the electron) and Z (atomic number) are exact, integer values, so they do not constrain the number of significant figures.

An atomic orbital can be populated by which of the following?

2 or less Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.

If a standing wave has 3 nodes, how many half-wavelengths does it have?

4 When n is the number of nodes in a standing wave, then n+1 is equal to the number of half-wavelengths.

An electron in an unknown energy level of a hydrogen atom transitions to the n=2 level and emits a photon with wavelength 410 nm in the process. What was the initial energy level? Use R∞=2.179×10^−18J for the hydrogen atom Rydberg constant. Use h=6.626×10^−34 Js for Planck's constant. Use c=2.998×10^8ms for the speed of light. Your answer should be a whole number.

6 Two equations will be required to solve this problem. Recall that the wavelength of a photon is related to its energy by λ=(hc)/E, where λ is the wavelength in meters, h is Plank's constant (6.626×10−^34 Js), and E is the energy of the photon in joules. First, convert the wavelength from nm to m: 410 nm × 1 m/ 10^9 nm =4.10×10^−7 m Next, rearrange the equation to solve for the energy of the photon: E=hcλ Substitute in the known values and solve: E= ((6.626×10−^34 Js)(2.998×10^8ms)) /4.10×10^−7 m E=4.845×10^−19 J The energy of the photon must be equal to the energy lost by the electron during its transition, according to the Rydberg equation: ΔE=R∞(1/ n21− 1/n22) Substitute in the known values and rearrange: 14−1n21=4.845×10−19 J2.179×10−18J=0.2223 Multiply all terms by n21: 0.25n21−1=0.2223n21 Combine the like terms and simplify: 0.25n21−0.2223n21=10.0277n21=1n21=10.0277=36.1n1=6.008 n1 must be a whole number because the energy levels are quantized. The calculated value of 6.008 is close enough to a whole number to be attributed to rounding errors and/or imprecise input values. Therefore, the correct answer is the nearest whole number, or 6.

A laser emits light with a frequency of 4.75×10^14 s−1. What is the wavelength of this radiation, in nm? Your answer should have three significant figures. Use c=2.998×10^8ms for the speed of light.

6.32 x 10 ^2 nm

What is the frequency of a particular type of radiation in Hertz given that the wavelength is 4.40×10^2nm? Use c=2.998×10^8ms for the speed of light. Report your answer in scientific notation Your answer should have three significant figures.

6.81 x 10^14 Hz Recall that the useful wave equation is: c=λ⋅ν, where λ is the wavelength, ν is the frequency, and c is the speed of light. First, convert the wavelength from nm to m: 4.40×102nm×1.00m1.00×109nm=4.40×10−7 m Next, rearrange the equation to solve for ν: v=cλ Substitute in the known values to solve: ν=2.998×108 ms4.40×10−7 mν=6.814×1014 s−1 Note that Hertz (Hz) is another name for inverse seconds (s−1). The answer should have three significant figures, so round to 6.81×1014 Hz

What is formed when two interfering waves cross?

A node is formed when two interfering waves cross.

For an atom, electrostatic potential is also called:

Coulomb potential These terms are synonymous, as Coulombs deal with electric charge. also called the electric field potential, potential drop, or the electrostatic potential

Bohr's model of the hydrogen atom, which restricts electrons to circular orbits around the nucleus parameterized by a single number, n, can best be applied to which other species?

He+ bc it lost an electron down to one. Bohr's model applies to any atom with one electron, such as He+,Li2+,Be3+, etc. Multielectron atoms like He are affected by repulsion between electrons and yield a more complicated pattern of energy levels.

Which of the following phenomena can only be explained by considering the wave nature of light?

Interference Early in the nineteenth century, Thomas Young demonstrated that light passing through narrow, closely spaced slits produced an interference pattern that could not be explained in terms of Newtonian particles, but could be easily explained in terms of waves. Phenomena such as reflection and refraction can be equally well explained in terms of light travelling as high-speed waves or as high-speed particles.

The Pauli exclusion principle states that:

No two electrons in an atom can have the same set of quantum numbers. It is the Pauli exclusion principle that states no two electrons in the same atom can have exactly the same set of four quantum numbers, which excludes electrons from having identical sets of quantum numbers.

Which of the following quantum numbers describes an electron in an atom? Select all that apply.

The magnetic quantum number (ml), the spin quantum number (ms), the principle quantum number (n), and the angular momentum quantum number(l) all describe an electron. Your answer:

Which of the following signifies the spatial orientation, i.e. direction, of an atomic orbital?

The magnetic quantum number, ml, signifies the spatial orientation of an atomic orbital.

The angular momentum quantum number, l, corresponds to:

The number of subshells, or l, describes the shape of the orbital Each value for the angular momentum quantum number will correspond specifically with s,p,d, or f orbitals, which each have their own distinct shapes.

What is the maximum wavelength of photon that will eject a ground state electron from a hydrogen atom?

The photon needs to have energy equal to the ionization energy of hydrogen, which, in joules, is 2.180 x 10^-18 J (found on most any ionization energy table). Find the maximum wavelength using E = hc/λ, where E = energy h = Planck's constant = 6.626 x 10^-34 J•s c = speed of light = 2.998 x 10^8 m/s λ = wavelength (in meters) Rearranging E = hc/λ to solve for λ gives λ = (hc) / E = { [(6.626 x 10^-34 J•s) x (2.998 x 10^8 m/s)] / (2.180 x 10^-18 J) } = 9.11 x 10^-8 m

An antinode is formed when there is constructive interference between two interfering waves. What is formed when there is destructive interference between two waves?

a node

An example of a standing wave is:

a vibrating string All of the other waves travel through space, but a vibrating string, on say a piano, will remain stationary. (the others were: a sound wave, electromagnetic radiation, and an ocean wave)

In two-dimensional standing waves, a node that sweeps out all radii at a constant angle is called a(n):

angular node All of the radii at a particular angle will generate a line that will essentially be the radius of the entire standing wave, which will be called an angular node.

As n increases, the distance between the energy levels:

as n increases the difference in energy between subsequent levels gets smaller while the separation between energy levels gets larger.

A two-dimensional standing wave can have:

both radial and angular nodes

The success of Bohr's model that demanded the scientific community's attention was its ability to:

calculate the Rydberg constant The Rydberg constant was one of the most precisely measured constants of the time, so when Bohr's model calculated this constant to be in excellent agreement with the experimentally determined value, it was impossible to deny the validity of his model for the hydrogen atom.

As the number of nodes increases, the energy of the wave ______________.

increases The energy of a standing wave increases with increasing number of nodes, and therefore also with increasing number of half-wavelengths.

Which of the following distinguishes the different shapes of orbitals?

l The angular momentum quantum number, l, distinguishes the different shapes of orbitals.

Which of the following quantum numbers does NOT define orbitals?

ms ms describes the intrinsic electron property known as "spin", while n,l, and ml define the orbital.

When assessing atoms with more than one proton, we must:

multiply the Rydberg constant by the nuclear charge We must incorporate Z, the nuclear charge, into the equation, as additional protons will introduce a stronger electromagnetic attraction and therefore alter the position of the electron's orbits.

The ground state for the hydrogen atom is represented by:

n=1 The ground state, which is the lowest possible energy, is n=1. It is followed by consecutive integers.

Which set of quantum numbers is invalid?

n=2,l=0,ml=−1,ms=12 Since l =0 indicates a s-orbital (sphere-shaped), there are no additional vector directions and the magnetic quantum number ml must also be zero. Therefore, the option n=2,l=0,ml=−1,ms=1/2 does not represent a valid set of quantum numbers.

Which of the following has the most energy? n=4,l=2 n=3,l=0 n=3,l=1 n=2,l=0

n=4,l=2 The quantum number n tells us the basic energy level and distance from the nucleus. Of these choices, n=4 would be the highest energy, narrowing our choice to A.

In the energy expression for hydrogen-like atoms, Z is equal to the:

nuclear charge The number of protons in the nucleus will be relevant in determining the energy of the electron, and it will be represented by the letter Z.

Given the following quantum numbers n=4,l=1,ml=−1,0,1, what is the subshell of the orbital?

p For ml values of −1,0 and +1, there are three possible orbitals in the shell which indicates a p subshell. __ l=0→ the s-subshell l=1→ the p-subshell l=2→ the d-subshell l=3→ the f-subshell

The model for the atom that was understood when Bohr made his contributions was called the:

planetary model It was called the planetary model because it was thought that the electrons orbiting the nucleus must resemble planets orbiting a star.

In the equation that predicts the change in energy of an electron, the n values must be:

positive integers The n values correspond to orbital values, which are the set of positive integers.

A system that restricts the number and type of waveforms by having fixed end points has been:

quantized

In two-dimensional standing waves, a node that sweeps out all angles at a constant radius is called a(n):

radial node A radial node consists of all the points with a particular radius, therefore will appear as a circle.

Maxwell's theory of electromagnetic radiation discredited which of the following?

the particle view of light Maxwell's theory of electromagnetic radiation discredited the particle view of light. James Clerk Maxwell showed that visible light was just a part of the vast electromagnetic spectrum, which includes many other forms of radiation.

Which of the following statements are true according to the Pauli exclusion principle?

there are a maximum of two electrons in each orbital no two electrons can have the same four electronic quantum numbers the two electrons in each orbital must have opposite spins _______ The Pauli Exclusion Principle states that, in an atom, no two electrons can have the same four electronic quantum numbers. This means that at least one of their n,l,ms,ml values must be different. The Pauli Exclusion Principle also implies that a maximum of two electrons can be found in one orbital, and the two electrons must have opposite spins.

For a three-dimensional standing wave, the nodes would be:

two-dimensional planes A node will have always have one fewer dimensions than the corresponding standing wave, so three dimensions for the wave means two dimensions for the node, hence a plane