Electronic Structure
Answer: D. The problem requires the MCAT favorite equation E = hc/λ, where h = 6.626 x 10^-34 J*s (Planck's constant), c = 3.00 x 10^8 m/s is the speed of light, and λ is the wavelength of the light. This question asks for the energy of one mole of photons, so we must multiply by Avogadro's number, Na = 6.02 x 10^23 1/mol. The setup is: E = hc/λ * Na 6.625 x 10^-34 J*s * 3 x 10^8 m/s * 6.02 x 10^23 1/mol 500 x 10^-9 m E = 2.39 x 10^5 J
An electron returns from an excited state to its ground state, emitting a photon at λ = 500 nm. What would be the magnitude of the energy change if one mole of these photons were emitted? (Note: h = 6.626 x 10^-34 J*s, Na = 6.02 x 10^23 1/mol) A. 3.98 x 10^-21 J B. 3.98 x 10^-19 J C. 2.39 x 10^3 J D. 2.39 x 10^5 J
Increases Increases
As n increases, the average distance of the electron from the nucleus _________________, and the energy _________________________ as well.
unique
Atomic absorption spectrum and atomic emission spectrum is ______________ for each element.
1. # orbitals = n^2 1^2 = 1 #orbitals = 1 l = 0 -> n-1 n-1 = 0 l = 0 m(l) = possible integers from -l to +l m(l) = 0 l = 0 ---> s-orbital #possible orbitals = 1 s-orbital 2. Only one s-orbital s-orbital can only fit 2 electrons in the subshell Total number of electrons in s-subshell = 2 3. #electrons in n=1 = (2n^2) (2(1^2)) = 2 #electrons in n=1 = 2
For n=1, find, 1. The number of possible orbitals 2. The number of electrons in each subshell 3. The total number of electrons in the shell
1. # orbitals = n^2 2^2 = 4 #orbitals = 4 l = 0 -> n-1 2-1 = 1 l = 0 or 1 m(l) = possible integers from -l to +l m(l) = 0 if l=0 m(l) = -1, 0, or +1 if l=1 l = 0 ---> s-orbital l = 1 ---> p-orbital One possible orbital in s-subshell (m(l) = 0) Three possible orbitals in p-subshell (m(l) = -1, 0, +1) 2. One s-orbital s-orbital can only fit 2 electrons in the subshell Three p-orbitals 2 electrons fit into each p-orbital Total number of electrons in s-subshell = 2 Total number of electrons in p-subshell = 6 3. #electrons in n=2 = (2n^2) (2(2^2)) = 8 #electrons in n=2 = 8
For n=2, find, 1. The number of possible orbitals 2. The number of electrons in each subshell 3. The total number of electrons in the shell
1. # orbitals = n^2 3^2 = 9 #orbitals = 9 l = 0 -> n-1 3-1 = 2 l = 0, 1, 2 m(l) = possible integers from -l to +l m(l) = 0 if l=0 m(l) = -1, 0, or +1 if l=1 m(l) = -2, -1, 0, 1, 2 if l=2 l = 0 ---> s-orbital l = 1 ---> p-orbital l = 2 ---> d-orbital One possible orbital in s-subshell (m(l) = 0) Three possible orbitals in p-subshell (m(l) = -1, 0, +1) Five possible orbitals in d-subshell (m(l) = -2, -1, 0, 1, 2) 2. One s-orbital s-orbital can only fit 2 electrons in the subshell Three p-orbitals 2 electrons fit into each p-orbital Five d-orbitals 2 electrons fit into each d-orbital Total number of electrons in s-subshell = 2 Total number of electrons in p-subshell = 6 Total number of electrons in d-subshell = 10 3. #electrons in n=3 = (2n^2) (2(3^2)) = 18 #electrons in n=3 = 18
For n=3, find, 1. The number of possible orbitals 2. The number of electrons in each subshell 3. The total number of electrons in the shell
1. # orbitals = n^2 4^2 = 16 #orbitals = 16 l = 0 -> n-1 4-1 = 3 l = 0, 1, 2, 3 m(l) = possible integers from -l to +l m(l) = 0 if l=0 m(l) = -1, 0, or +1 if l=1 m(l) = -2, -1, 0, 1, 2 if l=2 m(l) = -3, -2, -1, 0, 1, 2, 3 if l=3 l = 0 ---> s-orbital l = 1 ---> p-orbital l = 2 ---> d-orbital l = 3 ---> f-orbital One possible orbital in s-subshell (m(l) = 0) Three possible orbitals in p-subshell (m(l) = -1, 0, +1) Five possible orbitals in d-subshell (m(l) = -2, -1, 0, 1, 2) Seven possible orbitals in f-subshell (m(l) = -3, -2, -1, 0, 1, 2, 3) 2. One s-orbital s-orbital can only fit 2 electrons in the subshell Three p-orbitals 2 electrons fit into each p-orbital Five d-orbitals 2 electrons fit into each d-orbital Seven f-orbitals 2 electrons fit into each f-orbital Total number of electrons in s-subshell = 2 Total number of electrons in p-subshell = 6 Total number of electrons in d-subshell = 10 Total number of electrons in f-subshell = 14 3. #electrons in n=4 = (2n^2) (2(4^2)) = 32 #electrons in n=4 = 32
For n=4, find, 1. The number of possible orbitals 2. The number of electrons in each subshell 3. The total number of electrons in the shell
KE(photoelectron) = E(photon) - E° E° = 3.43 x 10^-19 J E(photon) = hν ν = c/λ E(photon) = h*(c/λ) λ = 625 nm = 6.25 x 10^-7 m E(photon) = 6.626 x 10^-34 J*s * (3 x 10^8 m/s/6.25 x 10^-7 m) E(photon) = 3.18 x 10^-19 J KE(photoelectron) = 3.18 x 10^-19 J - 3.43 x 10^-19 J KE(photoelectron) = -2.5 x 10^-20 J KE(photoelectron) is negative, so photon will not have enough energy to produce a photoelectron.
If a photon of wavelength 625 nm hits metallic cesium (work function 3.43 x 10^-19 J), will it be able to produce a photoelectron? If so, what is the velocity of the photoelectron produced?
3 eV * (1.60 x 10^-19 J) = 4.8 x 10^-19 J E = h*c/λ or λ = h*c/E λ = 6.626 x 10^-34 J*s * 3 x 10^8 m/s/4.8 x 10^-19 J λ = 4.14 x 10^-7 m = 414 x 10^-9 m = 414 nm
If an electron emits 3 eV of energy, what is the corresponding wavelength of the emitted photon? (Note: 1 eV = 1.60 x 10^-19 J, h = 6.626 x 10^-34 J*s)
If the photons have a frequency of 6.00 x 10^14 Hz, each photon has an energy of: Ep = hν = 4.14 x 10^-15 eV*s * 6.00 x 10^14 Hz = 2.48 eV Clearly then, any given photon has more than enough energy to allow an electron in the metal to overcome the 2.26 eV barrier. In fact, the maximum excess kinetic energy carried away by the electron turns out to be: KE = Ep - E° = 2.48 - 2.26 = 0.22 eV
If blue light of frequency 6.00 x 10^14 Hz is incident on rubidium (E° = 2.26 eV), will there be photoejection of electrons? If so, what is the maximum kinetic energy that an ejected electron will carry away? (Note: h = 6.626 x 10^-34 J*s = 4.14 x 10^-15 eV*s)
n=2 l=1: 2p: B, C, N, O, F, Ne n=3 l=0: 3s: Na, Mg n=5 l=3: 5f: Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr n=4 l=2 4d: Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd
If given the following quantum numbers, which element(s) do they likely refer to? 1. n=2 l=1 2. n=3 l=0 3. n=5 l=3 4. n=4 l=2
Frequency Threshold frequency Energy Frequency Threshold frequency Kinetic energy Energy Work function
If the _______________ of the photon is less than the _____________________ (f < f(T)), then no electron will be ejected from the metal, because the photons do not have sufficient ___________ to dislodge the electron from its atom. If the _________________ of the photon is greater than the _____________________ (f > f(T)), then a electron will be ejected. The maximum _____________________ of the ejected electron (photoelectron) is equal to the ______________ of the photon and the ____________________ of the metal.
Energy Work function Energy Energy Work function
If the _________________ of the photon is less than the ________________ of the metal (E(photon) < E°), then no electron will be ejected from the metal, because the photons do not have sufficient ___________ to dislodge the electron from its atom. If the ______________ of the photon is greater than the _____________ of the metal (E(photon) > E°), then a electron will be ejected.
Answer: C. To determine the speed of the electrons ejected, we must first calculate their kinetic energy: KE = E(photon) - E° E(photon) = hν = 6.626 x 10^-34 J*s * 1.0 x 10^14 Hz E(photon) = 6.626 x 10^-20 J KE = 6.626 x 10^-20 J - 6.622 x 10^-20 J = 4 x 10^-23 J KE = 1/2mv^2 v^2 = 2(4 x 10^-23 kg*m^2/s^2)/9.11 x 10^-31 kg v = 9370.997 m/s = 9.38 x 10^3 m/s
If the work function of a metal is 6.622 x 10^-20 J and a ray of electromagnetic radiation with a frequency of 1.0 x 10^14 Hz is incident on the metal, what will be the speed of the electrons ejected from the metal? (Note: h = 6.626 x 10^-34 J*s and mass of an electron = 9.11 x 10^-31 kg) A. 2.62 x 10^-6 m/s B. 1.07 x 10^-4 m/s C. 9.38 x 10^3 m/s D. 3.81 x 10^5 m/s
Position Momentum Momentum Position
If we want to assess the _________________ of an electron, the electron has to stop moving (thereby removing _______________). If we want to assess the ____________________ of an electron, the electron has to be moving (thereby changing its ___________________).
Electron Photocurrent Photoelectric effect
If you shine a light onto a metal, the photon will be able to knock a ______________ loose, causing a __________________ to flow. This is known as the _____________________ effect.
=
In a neutral atom, the # of protons _________ # of electrons.
The exact amount of energy
In order to get move an electron to a higher energy level, it must receive _____________________ energy in order to reach that level.
Principle Azimuthal/Angular Magnetic Spin
In quantum numbers: -n represents the ________________________ quantum number. -l represents the _________________________ quantum number. -ml represents the ______________________ quantum number -ms represents the ______________________ quantum number
s-subshell d-subshell s-subshell d-subshell
In regards to the electron configuration of transition metals, the __________ subshell becomes higher in energy than the __________ subshell. Because of this, when a transition metal becomes a cation, valence electrons are first removed from the _____________ subshell before removing electrons from the ______________ subshell.
The difference between the two energy levels will equal the amount of energy needed to move the electron. E1 = -2.18 x 10^-18 J E2 = E1/(2^2) = -2.18 x 10^-18 J/4 = -5.45 x 10^-19 J -2.18 x 10^-18 J = -21.8 x 10^-19 J 21.8 x 10^-19 - 5.45 x 10^-19 16.35 x 10^-19 J = 1.64 x 10^-18 J eV: E1 = -13.6 eV E2 = E1/(2^2) = -13.6 eV/4 = -3.4 eV 13.6 eV - 3.4 eV 10.2 eV
Say that we want to cause an electron to go from the first energy level (n=1) to the second energy level (n=2). How much energy do we need to give the electron in order to do that (Give the value in both joules and electron volts).
The difference between the two energy levels will equal the amount of energy needed to move the electron. E1 = -2.18 x 10^-18 J E3 = E1/(2^2) = -2.18 x 10^-18 J/9 = -2.42 x 10^-19 J -2.18 x 10^-18 J = -21.8 x 10^-19 J 21.8 x 10^-19 - 2.42 x 10^-19 19.38 x 10^-19 J = 1.94 x 10^-18 J eV: E1 = -13.6 eV E3 = E1/(3^2) = -13.6 eV/9 = -1.51 eV 13.6 eV - 1.51 eV 12.09 eV
Say that we want to cause an electron to go from the first energy level (n=1) to the third energy level (n=3). How much energy do we need to give the electron in order to do that (Give the value in both joules and electron volts).
Answer: B. Because the electron is moving into the n=1 shell, the only subshell available is the 1s subshell, which eliminates (C.) and (D.). There will be some energy change, however, as the electron must lose energy to return to the minimum-energy ground-state. That will require emitting radiation in the form of a photon.
Suppose an electron falls from n=4 to its ground state, n=1. Which of the following effects is most likely? A. A photon is absorbed B. A photon is emitted C. The electron moves into a p-orbital D. The electron moves into a d-orbital
Answer: A. The MCAT covers the topics in this chapter qualitatively more often than quantitatively. It is critical to be able to distinguish the fundamental principles that determine electron organization, which are usually known by the names of the scientists who discovered or postulated them. The Heisenberg uncertainty principle, (B.), refers to the inability to know the momentum and position of a single electron simultaneously. The Bohr model, (C.), was an early attempt to describe the behavior of the single electron in a hydrogen atom. The Rutherford model, (D.), described a dense, positively charged nucleus. The element shown here, phosphorous, is often used to demonstrate Hund's rule because it contains a half-filled p subshell. Hund's rule explains that electrons fill empty orbitals first before doubling up electrons in the same orbital.
Suppose that an atom fills its orbitals as shown. Such an electron configuration most clearly illustrates which of the following laws of atomic physics? A. Hund's rule B. Heisenberg uncertainty principle C. Bohr model D. Rutherford model
Position Momentum Same time Position/Momentum Momentum/Position
The Heisenberg uncertainty principle is a principle of quantum mechanics that states that the ________________ and ________________ of a particle cannot be accurately measured at the ____________________. If you know the _____________________ of a particle, then you do not know the _________________ of the particle, and vice versa.
to work full-time/part-time
The ________________ is the energy (or work) required to remove an electron completely from a metal surface.
Azimuthal/Angular Quantum number Spin Quantum number Principle Quantum number Magnetic Quantum number
The ____________________ quantum number indicates the shape that an orbital will take. The ____________________ quantum number indicates the "spin" of an electron (though the electron is not actually spinning. The ___________________ quantum number indicates the main energy level that the electrons of an atom occupy. The __________________ quantum number indicates the orientation of an orbital around a nucleus.
Lyman series Balmer series Paschen series Brackett series
The ______________________ is a set of spectral lines that appear in the UV region when a hydrogen atom undergoes a transition from energy levels n>1 to n=1. The _____________________ is a set of spectral lines that appear in the visible light region when a hydrogen atom undergoes a transition from energy levels n>2 to n=2. The ______________________ is a set of spectral lines that appear in the infrared region when a hydrogen atom undergoes a transition from energy levels n>3 to n=3. The ___________________ is a set of spectral lines that appear in the infrared region when a hydrogen atom undergoes a transition from energy levels n>4 to n=4.
energy absorb/emit E = Energy for transition E1 = Rydberg unit of energy (-2.18 x 10^-18 J/-13.6 eV) n(i) = initial (starting) energy level n(f) final (ending) energy level
The following equation is used to determine the ____________ that an electron needs to __________________ to jump from one energy state to another: E = E1 * [(1/(n(i)^2)) - (1/(n(f)^2))] E = _______________________ E1 = ____________________________ n(i) = _____________________________ n(f) = ______________________________
Energy Wavelength Energy of the photon Planck's constant (6.626 x 10^-34 J*s/4.14 x 10^-15 eV*s) Speed of light (3 x 10^8 m/s) Wavelength of the photon
The following equation is used to determine the _________________ of a photon when we are given ________________________. E(photon) = h*(c/λ) E(photon) = _____________________ h = _____________________ c = ______________________ λ = ________________________
Energy Frequency Energy of the photon Planck's constant (6.626 x 10^-34 J*s/4.14 x 10^-15 eV*s) frequency of the photon
The following equation is used to determine the __________________ of a photon when we are given ___________________: E(photon) = hν E(photon) = ______________________ h = _______________________ ν = __________________________
Energy Energy level E(n) = The energy of an electron at an energy level of n E1 = Rydberg unit of energy (-2.18 x 10^-18 J) n = the energy level of the valence electron
The following equation is used to determine the __________________ of an electron at a certain ____________________: E(n) = E1/(n^2) E(n) = _______________________ E1 = _________________________ n = __________________________
Heisenberg uncertainty principle Δx = uncertainty in position Δp = uncertainty in momentum h = Planck's constant (6.626 x 10^-34 J*s/4.14 x 10^-15 eV*s)
The following equation is used to determine the ________________________________: Δx * Δp > h/4π Δx = ______________________ Δp = _______________________ h = ____________________________
Kinetic energy Kinetic energy Mass Velocity
The following equation is used to find _____________________________: KE = (1/2)mv^2 KE = ________________________ m = ______________ v = _________________
Work function of the metal Planck's constant (6.626 x 10^-34 J*s/4.14 x 10^-15 eV*s) Threshold frequency of metal (given)
The following equation is used to find the ______________________ of a __________________: E° = h*f(T) E° = ___________________ h = ______________________ f(T) = ________________________
angular momentum electron v = velocity of an electron n = energy level of the valence electron h = Planck's constant (6.626 x 10^-34 J*s/4.14 x 10^-15 eV*s) m = mass of electron (9.11 x 10^-31 kg) r = atomic radius
The following equation is used to find the ______________________ of a ____________________: vmr = (nh)/(2π) v = ________________________ n = _________________________ h = _________________________ m = _______________________ r = ________________________
Atomic radii r(n) = atomic radius of an atom at a particular energy level n = energy level the electron is at r1 = atomic radius of the smallest orbit in the Bohr model (5.3 x 10^-11 m)
The following equation is used to find the _________________________ of an atom using the Bohr model: r(n) = n^2 * r1 r(n) = _____________________ n = ______________________ r1 = __________________________
Kinetic energy of the photoelectron ejected Energy of the photon Work function of the metal
The following equation is used to find the __________________________________ of a photoelectron: KE(photoelectron) = E(photon) - E° KE(photoelectron) = ______________________________ E(photon) = __________________________ E° = _________________________________
Linear momentum p = linear momentum m = mass v = velocity
The following is an equation used for ________________________: p=mv p = _____________________ m = _____________________ v = ____________________
Rydberg unit of energy (E1) in joules
The following is the value of ___________________: -2.18 x 10^-18 J
The speed of light (c)
The following is the value of ____________________: 3 x 10^8 m/s
Rydberg's constant
The following is the value of _____________________: 1.09 x 10^7 1/m
Rydberg unit of energy (E1) in electron volts
The following is the value of _______________________: -13.6 eV
The mass of an electron
The following is the value of _______________________: 9.11 x 10^-31 kg
Planck's constant in J*s (h)
The following is the value of __________________________: 6.626 x 10^-34 J*s
The atomic radius of the smallest orbit in the Bohr model (r1)
The following is the value of ____________________________: 5.3 x 10^-11 m
Planck's constant in eV*s (h)
The following is the value of ______________________________: 4.14 x 10^-15 eV*s
λ = wavelength of photon R = Rydberg's constant (1.097 x 10^7 1/m) n(f) = final (ground) energy state n(i) = initial (excited) energy state
The folowing equation is used to determine the wavelength of the photon that is emitted when an electron transitions from a higher energy state to a lower energy state: 1/λ = R * [(1/(n(f)^2)) - (1/(n(i)^2))] λ = ___________________________ R = _____________________________ n(f) = __________________________ n(i) = ____________________________
Inversely proportional Increases Decreases
The uncertainties of momentum and position of a particle in the Heisenberg uncertainty principle are ___________________________ to each other. So, if the value of one of the uncertainties _________________, the value of the the other uncertainty _____________________.
Joules (J)
The unit of measurement __________ is also equal to kg*(m^2/s^2)
Joules: E= -E1[(1/(n(i)^2) - 1/(n(f)^2)) E = -2.18 x 10^-18 * [1/(2^2) - 1/(4^2)] = -4.09 x 10^-19 J Electron volts: E = -13.6 * [1/4 - 1/16] = -2.55 eV In both cases, the value is negative, indicating that energy is absorbed. This is consistent with an electron moving from a lower to a higher shell.
The valence electron in a lithium atom jumps from energy level n=2 to n=4. What is the energy of this transition in joules? In eV? (Note: E1 = 2.18 x 10^-18 J = 13.6 eV)
Magnetic quantum number Azimuthal/Angular quantum number Principle quantum number Spin quantum number
The value of ___________________________ quantum number are dependent on the value of l. It equals any integral value that goes from -l to +l. The value of ___________________________ quantum number are dependent on the value of n. Values will be a range between 0 to n-1. The value of ____________________________ quantum number is a positive integer, meaning the value of it will equal to 1, 2, 3, etc. The value of ____________________________ quantum number are either +1/2 or -1/2.
False. Small changes, such as protonation and deprotonation, change in oxidation state or bond order, and others may cause dramatic changes in light absorption in a material.
True or False: Small changes in chemical structure only minimally impact light absorption and emission patterns.
True
True or false, the line spectrum is unique for every element on the periodic table.
Visible lights Ultraviolet lights Infrared lights
Wavelengths from 380 nm to 740 nm are in the range of ___________________. Wavelengths below 380 nm fall into the range of ____________________, which we cannot see. Wavelengths above 740 nm fall into the range of ________________, which we cannot see.
-Principle quantum number (n) -Azimuthal/Angular quantum number (l) -Magnetic quantum number (ml) -Spin quantum number (ms)
What are the 4 quantum numbers of an atom?
Fluorescence is a special stepwise photon emission in which an excited electron returns to the ground state through one or more intermediate excited states. Each energy transition releases a photon of light. With smaller energy transitions than the initial energy absorbed, these materials can release photons of light in the visible range.
What causes fluoresence?
The energy differences between ground-state electrons and higher-level electron orbits determine the frequencies of light a particular material absorbs (its absorption spectrum).
What determines the absorption spectrum of a single atom?
The threshold frequency depends on the chemical composition of a material (that is, the identity of the metal).
What does the threshold frequency depend upon?
The accumulation of moving electrons creates a current during the photoelectric effect.
What electrical phenomenon results from the application of the photoelectric effect?
r(n) = n^2 * r1 r1 = 5.3 x 10^-11 m n = 1 r(n) = 1^2 * 5.3 x 10^-11 m r(n) = 5.3 x 10^-11 m r(n) = n^2 * r1 r1 = 5.3 x 10^-11 m n = 2 r(n) = 2^2 * 5.3 x 10^-11 m r(n) = 2.12 x 10^-10 m r(n) = n^2 * r1 r1 = 5.3 x 10^-11 m n = 3 r(n) = 3^2 * 5.3 x 10^-11 m r(n) = 4.77 x 10^-10 m
What is the atomic radius of an atom with its valence electron at an energy level of n=1? What is the atomic radius of an atom with its valence electron at an energy level of n=2? What is the atomic radius of an atom with its valence electron at an energy level of n=3?
n=1 E(n) = E1/(n^2) E1 = -2.18 x 10^-18 J -2.18 x 10^-18 J/1.6 x 10^-19 J = -13.6 eV E(n) = -13.6 eV/(1^2) E(n) = -13.6 eV n=2 E(n) = E1/(n^2) E1 = -2.18 x 10^-18 J -2.18 x 10^-18 J/1.6 x 10^-19 J = -13.6 eV E(n) = -13.6 eV/(2^2) E(n) = -3.4 eV n=3 E(n) = E1/(n^2) E1 = -2.18 x 10^-18 J -2.18 x 10^-18 J/1.6 x 10^-19 J = -13.6 eV E(n) = -13.6 eV/(3^2) E(n) = -1.51 eV
What is the energy of a valence electron at an energy level of n=1 in electron volts? What is the energy of a valence electron at an energy level of n=2 in electron volts? What is the energy of a valence electron at an energy level of n=3 in electron volts?
n=1 E(n) = E1/(n^2) = -2.18 x 10^-18 J/(1^2) E(n) = -2.18 x 10^-18 J n=2 E(n) = E1/(n^2) = -2.18 x 10^-18 J/(2^2) E(n) = -5.45 x 10^-19 J n=3 E(n) = E1/(n^2) = -2.18 x 10^-18 J/(3^2) E(n) = -2.42 x 10^-19 J
What is the energy of a valence electron at an energy level of n=1 in joules? What is the energy of a valence electron at an energy level of n=2 in joules? What is the energy of a valence electron at an energy level of n=3 in joules?
Answer: C. For any value of n, there will be a maximum of 2n^2 electrons; that is, two per orbital. This can also be determined from the periodic table. There are only two elements (H and He) that have valence electrons in the n=1 shell. Eight elements (Li to Ne) have valence electrons in the n=2 shell. This is the only equation that matches the pattern.
What is the maximum number of electrons allowed in a single atomic energy level in terms of the principal quantum number n? A. 2n B. 2n + 2 C. 2n^2 D. 2n^2 + 2
n=1 r(n) = n^2 * r1 = 1^2 * 5.3 x 10^-11 m r(n) = 5.3 x 10^-11 m mvr = nh/2π v = nh/2πmr v = 1 * 6.626 x 10^-34 J*s/2π * 9.11 x 10^-31 kg * 5.3 x 10^-11 m v = 2184124.128 m/s v = 2.18 x 10^6 m/s n=2 r(n) = n^2 * r1 = 2^2 * 5.3 x 10^-11 m r(n) = 2.12 x 10^-10 m mvr = nh/2π v = nh/2πmr v = 2 * 6.626 x 10^-34 J*s/2π * 9.11 x 10^-31 kg * 2.12 x 10^-10 m v = 1092062.064 m/s v = 1.09 x 10^6 m/s n=3 r(n) = n^2 * r1 = 3^2 * 5.3 x 10^-11 m r(n) = 4.77 x 10^-10 m mvr = nh/2π v = nh/2πmr v = 3 * 6.626 x 10^-34 J*s/2π * 9.11 x 10^-31 kg * 4.77 x 10^-10 m v = 728041.3761 m/s v = 7.28 x 10^5 m/s
What is the velocity of an electron at an energy level of n=1? What is the velocity of an electron at an energy level of n=2? What is the velocity of an electron at an energy level of n=3?
2-1 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(1^2) - 1/(2^2)) 1/λ = 8227500 1/m λ = 1.22 x 10^-7 m = 122 x 10^-9 m = 122 nm Ultraviolet 3-1 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(1^2) - 1/(3^2)) 1/λ = 9751111.111 1/m λ = 1.03 x 10^-7 m = 103 x 10^-9 m = 103 nm Ultraviolet 4-1 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(1^2) - 1/(4^2)) 1/λ = 10284375 1/m λ = 9.72 x 10^-8 m = 97.2 x 10^-9 m = 97 nm Ultraviolet 4-3 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(3^2) - 1/(4^2)) 1/λ = 533263.8889 1/m λ = 1.875 x 10^-6 m = 1875 x 10^-9 m = 1875 nm Infrared
What is the wavelength of an electron in hydrogen going from an energy level of n=2 to n=1? Is the light emitted categorized as visible light, infrared light, or ultraviolet light? What is the wavelength of an electron in hydrogen going from an energy level of n=3 to n=1? Is the light emitted categorized as visible light, infrared light, or ultraviolet light? What is the wavelength of an electron in hydrogen going from an energy level of n=4 to n=1? Is the light emitted categorized as visible light, infrared light, or ultraviolet light? What is the wavelength of an electron in hydrogen going from an energy level of n=4 to n=3? Is the light emitted categorized as visible light, infrared light, or ultraviolet light?
ground energy state excited energy state temporary excited energy state ground energy state photon light photon
When an electron undergoes absorption, it will go from a ___________ energy state to a ___________ energy state. Absorption is only _________________; it will not stay in the _____________ state forever. It will eventually return to the _______________ state, which is referred to as emission. When an electron undergoes emission, it releases a ______________, which causes the electron to emit ______________. The ______________ will have a certain wavelength related to the energy levels it drops from.
s subshell p subshell d subshell f subshell
When l=0, it indicates the presence of a _______ subshell. When l=1, it indicates the presence of a ________ subshell. When l=2, it indicates the presence of a ________ subshell. When l=3, it indicates the presence of a ________ subshell.
Answer: D. The only answer choice without unpaired electrons in its ground state is helium. Recall from the chapter that a diamagnetic substance is identified by the lack of unpaired electrons in its shell. A substance without unpaired electrons, like helium, cannot be magnetized by an external magnetic field and is actually slightly repelled. Elements that come at the end of a block (Group IIA, the group containing Zn, and the noble gases, most notably) have only paired electrons.
Which of the following atoms only has paired electrons in its ground state? A. Sodium B. Iron C. Cobalt D. Helium
Answer: C. The limitations placed by the Heisenberg uncertainty principle are caused by limitations inherent in the measuring process: if a particle is moving, it has momentum, but trying to measure that momentum necessarily creates uncertainty in the position. Even if we had an exact definition of the meter, as in(A.), or perfect measuring devices, as in (B.), we still wouldn't be able to measure position and momentum simultaneously and exactly.
Which of the following best explains the inability to measure position and momentum exactly and simultaneously according to the Heisenberg uncertainty principle? A. Imprecision in the definition of the meter and kilogram B. Limits on accuracy of existing scientific instruments C. Error in one variable is increased by attempts to measure the other D. Discrepancies between the masses of nuclei and of their component particles
Answer: B. For an electron to gain energy, it must absorb energy from the photons to jump up to a higher energy level. There is a bigger jump between n=2 and n=6 than there is between n=3 and n=4.
Which of the following electronic transitions would result in the greatest gain in energy for a single hydrogen electron? A. An electron moves from n=6 to n=2 B. An electron moves from n=2 to n=6 C. An electron moves from n=3 to n=4 D. An electron moves from n=4 to n=3
Answer: B. This formula describes the number of electrons in terms of the azimuthal quantum number l, which ranges from 0 to n-1, with n being the principal quantum number.
Which of the following equations describes the maximum number of electrons that can fit a subshell? A. 2l + 2 B. 4l +2 C. 2l^2 D. 2l^2 +2
Answer: A. Remember that when electrons are removed from an element, forming a cation, they will be removed from the subshell with the highest n-value first. Zn has 30 electrons, so it would have an electron configuration of 1s(2)2s(2)2p(6)3s(2)3p(6)4s(2)3d(10). The 4s subshell has the highest principal quantum number, so it is emptied first, forming 1s(2)2s(2)2p(6)3s(2)3p(6)4s(0)3d(10). (B.) implies the electrons are pulled out of the d-orbital, (C.) presents the configuration of the uncharged zinc atom, and (D.) shows the configuration that would exist if four electrons were removed.
Which of the following is the correct electron configuration for Zn(2+)? A. 1s(2)2s(2)2p(6)3s(2)3p(6)4s(0)3d(10) B. 1s(2)2s(2)2p(6)3s(2)3p(6)4s(2)3d(8) C. 1s(2)2s(2)2p(6)3s(2)3p(6)4s(2)3d(10) D. 1s(2)2s(2)2p(6)3s(2)3p(6)4s(0)3d(8)
Answer: B. The azimuthal quantum number l cannot be higher than n-1, ruling out (A.). The m(l) number, which describes the chemical's magnetic properties, can only be an integer value between -l and +l. It cannot be equal to +/- 1 if l = 0; this would imply that an s orbital has three subshells (-1, 0, +1) when we know it can only have one. This rules out (C.) and (D.).
Which of the following quantum number sets is possible? A. n=2, l=2, m(l)=1, m(s)=+1/2 B. n=2, l=1, m(l)=-1, m(s)=+1/2 C. n=2, l=0, m(l)=-1, m(s)=-1/2 D. n=2, l=0, m(l)=1, m(s)=-1/2
Answer: B. When dealing with ions, you cannot directly approach electronic configurations based on the number of electrons they currently hold. First examine the neutral atom's configuration, and then determine which electrons are removed. Due to the stability of half-filled d-orbitals, neutral chromium assumes the electron configuration of [Ar] 4s(1)3d(5). Mn must lose one electron from its initial configuration to become the Mn+ cation. That electron would come from the 4s subshell according to the rule that the first electron removed comes from the highest energy shell. Fe must lose two electrons to become Fe(2+). They'll both be lost from the same orbital; the only way Fe(2+) could hold the configuration in the question stem would be if one d-electron and one s-electron were lost together.
Which of the following species is represented by the electron configuration 1s(2)2s(2)2p(6)3s(2)3p(6)4s(1)3d(5)? I. Cr II. Mn+ III. Fe(2+) A. I only B. I and II only C. II and III only D. I, II, and III
Both O and O(2-) have fully filled 1s and 2s orbitals. O has four electrons in the 2p subshell; two are paired, and the other two have their own orbital. O(2-) has six electrons in the 2p subshell, all of which are paired in the three p-orbitals.
Write out and compare an orbital diagram for a neutral oxygen (O) atom and an O(2-) ion.
Aufbau principle Pauli Exclusion Principle Hund's Rule
____________________ is the concept that electrons fill energy levels in order of increasing energy, completely filling one sublevel before beginning to fill the next. _____________________ is the concept that no 2 electrons in an atom can have the same 4 quantum numbers. ____________________ is the concept that electrons will fill into separate orbitals with parallel spins before pairing in an orbital to minimize electron repulsion.
Ground state Excited state
____________________ is the energy state of an atom that in which it is at its lowest energy. ___________________ is the energy state of an atom when at least one electron has moved to a subshell of higher than normal energy.
Absorption Emission
_____________________ is the process of an electron absorbing energy and jumping to a higher energy level. ____________________ is the process of an electron emitting light, which causes the electron to fall to a lower energy level.
Fluoroescence
_______________________ is the process in which the electrons of certain substances are excited to higher energy levels by high-frequency photons, and then emit visible light as the energy is released in two or more steps back to the ground state.
Photon
A ____________ is a particle of light and is considered to be massless.
Line spectrum
A _______________________ is a spectrum of specific colors of light emitted when an electron goes from an excited state to a ground state.
paramagnetic attracted to diamagnetic repelled by
A __________________________ element is an element that has at least one or more orbitals with unpaired electrons, causing it to be __________________________ a magnetic field. A _________________________ element is an element that has only paired electrons in its orbtials, which produces
E = h*c/λ 662 nm = 662 x 10^-9 m = 6.62 x 10^-7 m E = 6.626 x 10^-34 J*s * 3 x 10^8 m/s/6.62 x 10^-7 m E = 3.00 x 10^-19 J
Calculate the energy of a photon of wavelength 662 nm. (Note: h = 6.626 x 10^-34 J*s)
dramatic small
Changes in molecular structure can cause _________________ shifts in absorption patterns of a substance, even _______________ changes have this effect.
Answer: A. The terms in the answer choices refer to the magnetic spin of the two electrons. The quantum number m(s) represents this property as a measure of an electron's intrinsic spin. These electrons' spins are parallel, in that their spins are aligned in the same direction (m(s) = +1/2 for both species).
Consider the two sets of quantum numbers shown in the table, which describe two different electrons in the same atom. Which of the following terms best describes these two electrons? A. Parallel B. Opposite C. Antiparallel D. Paired
n=3 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(2^2) - 1/(3^2)) 1/λ = 1523611.111 1/m λ = 6.56 x 10^-7 m = 656 x 10^-9 m = 656 nm It would emit a red light, since the wavelength will be 656 nm. n=4 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(2^2) - 1/(4^2)) 1/λ = 2056875 1/m λ = 4.86 x 10^-7 m = 486 x 10^-9 m = 486 nm It would emit a greenish light, since the wavelength will be 486 nm. 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(2^2) - 1/(5^2)) 1/λ = 2303700 1/m λ = 4.34 x 10^-7 m = 434 x 10^-9 m = 434 nm It would emit a blue light, since the wavelength will be 434 nm. 1/λ = R * (1/(n(f)^2) - 1/(n(i)^2)) 1/λ = 1.097 x 10^7 1/m * (1/(2^2) - 1/(6^2)) 1/λ = 2437777.778 1/m λ = 4.10 x 10^-7 m = 410 x 10^-9 m = 410 nm It would emit a violet light, since the wavelength will be 410 nm.
Considering the line spectrum of hydrogen shown, what color of light would be emitted if an excited electron fell from n=3 to n=2? What about from n=4 to n=2? What about from n=5 to n=2? What about from n=6 to n=2?
-P in PO4(3-): s: 2 p: 6 d: 2 f: 0 total: 10 -O in PO4(3-) s: 2 p: 6 d: 0 f: 0 total: 8 -Ir: s: 2 p: 0 d: 7 f: 0 total: 9 -Cf: s: 2 p: 0 d: 0 f: 10 total: 12
Determine how many valence electrons come from each subshell in the following atoms: -P in PO4(3-) -O in PO4(3-) -Ir -Cf
-Fe(2+): Paramagnetic -Ag+: Diamagnetic -Hg: Diamagnetic -B: Paramagnetic -Na+: Diamagnetic -Xe: Diamagnetic -Cu+: Diamagnetic F-: Diamagnetic Y: Paramagnetic Mg: Diamagnetic O(2-): Diamagnetic As: Paramagnetic
Determine whether or not the following are diamagnetic or paramagnetic: -Fe(2+) -Ag+ -Hg -B -Na+ -Xe -Cu+ -F- -Y -Mg -O(2-) -As
When electrons transition from a higher-energy state to a lower-energy state, they will experience photon emission.
During which electronic transitions is photon emissions most common?
Photon emission two more
Fluorescence is a special kind of _______________________ in which an excited electron returns to the ground state through ________ or _________ intermediate excited states.
Zero Attractive force
For an electron where its energy level is n=infinity, the electron has an energy value of _________, meaning that there is no _______________________ acting on the electron.
Divide the value of energy in joules by 1.6 x 10^-19 J Multiply the value of energy in electron volts by 1.6 x 10^-19 J
How do you convert joules into electron volts? How do you convert electron volts into joules?
The work function describes the minimum amount of energy necessary to emit an electron. Any additional energy from a photon will be converted to excess kinetic energy during the photoelectric effect.
How does the work function relate to the energy necessary to emit an electron from a metal?
Cr: [Ar] 4s(1)3d(5) He: 1s(2) Ag: [Kr] 5s(1)4d(10) Ca: [Ar] 4s(2) Ar: [Ne] 3s(2)3p(6) Si: [Ne] 3s(2)3p(2) Au: [Xe] 6s(1)4f(14)5d(10) C: [He] 2s(2)2p(2) Br: [Ar] 4s(2)3d(10)4p(5) Mo: [Kr] 5s(1)4d(5)
Identify the electron configuration of the following elements: -Cr -He -Ag -Ca -Ar -Si -Au -C -Br -Mo
Cl-: [Ne] 3s(2)3p(6) Fe(2+): [Ar] 3d(6) Cr(3+): [Ar] 3d(3) O-: [He] 2s(2)2p(5) Ba(2+): [Kr] 5s(2)4d(10)5p(6) H-: 1s(2) S(2-): [Ne] 3s(2)3p(6) Pt(2+): [Xe] 4f(14)5d(8) Be(2+): 1s(2) Cu+: [Ar] 3d(10)
Identify the electron configuration of the following: -Cl- -Fe(2+) -Cr(3+) - O- -Ba(2+) -H- -S(2-) -Pt(2+) -Be(2+) -Cu+
KE(photoelectron) = E(photon) - E° E° = 3.43 x 10^-19 J E(photon) = hν (ν = c/λ) E(photon) = h*(c/λ) 525 nm = 5.25 x 10^-7 m = 6.626 x 10^-34 J*s * (3 x 10^8 m/s/5.25 x 10^-7 m) E(photon) = 3.79 x 10^-19 KE(photoelectron) = 3.79 x 10^-19 J - 3.43 x 10^-19 J KE(photoelectron) = 3.6 x 10^-20 J The KE of the photoelectron is positive, so a photoelectron will be produced. 3.6 x 10^-20 J = (1/2)mv^2 m(electron) = 9.11 x 10^-31 kg 3.6 x 10^-20 kg*(m^2/s^2) = (1/2)(9.11 x 10^-31 kg)*v^2 7.2 x 10^-20 kg*(m^2/s^2) = (9.11 x 10^-31 kg) * v^2 7.9 x 10^10 (m/s)^2 = v^2 sqrt(7.9 x 10^10 (m/s)^2) = sqrt(v^2) v = 2.8 x 10^5 m/s
If a photon of wavelength 525 nm hits metallic cesium (work function = 3.43 x 10^-19 J), will it be able to produce a photoelectron? If so, what is the velocity of the photoelectron produced?
Both these molecules have unfilled valence electron shells with relatively few paired electrons; therefore, they are paramagnetic.
Magnetic resonance angiography (MRA) is a technique that can resolve defects like stenotic (narrowed) arteries. A contrast agent gadolinium or manganese injected into the blood stream interacts with the strong magnetic fields of the MRI device to produce such images. Based on their orbital configurations, are these contrast agents paramagnetic or diamagnetic?
Smallest E3>E2>E1
Since the quantities of energy associated with electrons at certain energy levels are negative, the highest energy level has the __________________ negative value of energy. E__ > E__ > E__
s subshell d subshell d subshell
Some transition metals will demote an electron from the __________ subshell to the _____________ subshell in order to stabilize the ___________ subshell, such is the case with transition metals such as manganese and copper.
