Chem 1050
The Electronic Structure of Atoms
Fall 2010
Text: Petrucci Herring Madura Bissonnette 10 th Edition Chapter 8
Exercises:
1, 9, 11, 13, 17, 19, 25, 27, 29(a), 29(b), 31, 33, 35, 37, 39, 43, 45, 49, 57, 59, 61,
71, 75, 77, 79, 81, 83, 87, 91(b), 91(c), 105
Text: Petrucci Harwood Herring Madura 9 th Edition Chapter 8
Exercises:
1, 9, 11, 13, 17, 19, 27, 29 (a,b) 31, 33, 39, 57, 59, 75, 77, 79, 81, 83, 87.
Additional Problems:
1.
Define or explain the following properties of electromagnetic waves: frequency, wavelength,
velocity and intensity.
2.
The green light emitted by barium atoms in a Bunsen flame has a wavelength of 553.5 nm. (a)
Calculate its frequency in hertz. (b) Calculate the energy of one photon of this light in joules.(c)
What would be the total energy of one mole of these photons in kilojoules?
3.
NO 2(g) is a major component of smog. It undergoes photodissociatio n (decomposes in the
presence of sunlight) to form two very reactive species, NO(g) and O(g), which react further with
other components of smog. The photodissociation energy of NO2 is 305 kJ mol-1.
(a)
Write a thermochemical equation to describe the photodissociation of NO2.
(b)
Calculate the photodissociation energy (in joules) of one molecule of NO2.
(c)
In order to undergo photodissociation, a molecule of NO2 must absorb a photon whose
energy is equal to or greater than its photodissociation energy. Calculate the wavelength
in nanometers of a photon which has just enough energy to photodissociate a molecule
of NO 2.
(d)
Predict whether or not a photon of wavelength 325 nanometers has sufficient energy to
photodissociate a molecule of NO2. Give your reasoning or show appropriate
calculations.
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4.
A photon with a wavelength of 0.242 :m has just enough energy to ionize a sodium atom. This
process can be described by the following equation:
Na(g) + energy 6 Na+(g) + e(a)
(b)
Calculate the ionization energy of one sodium atom.
Calculate the ionization energy of one mole of sodium atoms.
5.
Sketch an energy level diagram for a hydrogen electron using the Bohr model for all energy levels
from n = 1 to n = 4. On your diagram, indicate all possible pathways in which the electron can
drop from n = 4 to n = 1. How many photons will be emitted for each pathway?
6.
(a)
A hydrogen electron makes a transition from n = 2 to n = 5.
(i)
(ii)
(b)
7.
Is a photon emitted or absorbed during this transition?
Calculate the energy, frequency and wavelength (in nm) of the photon.
An electron in a hydrogen atom with n = 3 absorbs a photon of wavelength 1.005 microns.
Calculate the value of n for the electron in its final state.
Consider the Bohr hydrogen atom. Determine whether or not
(a)
(b)
an allowed energy level exists with E = !9.684 x 10G21 J
an allowed energy level exists with a radius of 1.00 nm.
8.
Calculate the ground state energy and radius of the electron in Li2+ using the Bohr model. How
do these values compare to those of the Bohr hydrogen atom?
9.
The photoelectric effect:
(a)
(b)
10.
Explain the terms threshold frequency and work function (threshold energy).
Explain why the number of electrons photo ejected from the surface of a metal depends
on the intensity of the incident light but the kinetic energy of the electrons depends on the
frequency of the incident light.
The properties of atomic orbitals are completely described by three quantum numbers (n, l, and
ml).
(a)
What are the names of these quantum numbers and what properties of atomic orbitals do
they describe?
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(b)
(c)
Identify the type of orbitals described by the following combinations of n and l (eg. 2s, 4d,
etc.). Indicate how many similar orbitals exist in a sub-shell for each orbital type. (i) n =
3, l = 2 (ii) n = 5, l = 0 (iii) n=7, l = 3 (iv) n= 2, l = 1
For each type of sub-shell listed below, determine the quantum numbers (n, l, ml) of each
orbital present. (i) 3p (ii) 4s (iii) 5d (iv) 6f
11.
An electron in an atom has 4 quantum numbers (n, l, ml, ms,). Identify impossible sets of quantum,
numbers by circling the offender.(3, 1,+2, +1/2) (5, 4, -4, +1)
(2, 2, 0, -1/2 ) (0, 1, +1, +1/2) (7, 2, -1, +1/2)
12.
Explain the significance of each part of the symbol 3pz2
13.
Orbitals can differ in size, shape and spatial orientation. What is the difference between the following orbitals (a) the 1s and 2s (b) 2px and the 2py.
14.
List all possible values of the four quantum numbers for
(a)
(b)
15.
each electron in a ground state lithium atom.
a 4p electron . Note: the quantum numbers of an electron are independent of the type of
atom.
Write ground state electron configurations in spdf notation for the following neutral atoms. Use
shorthand for elements found in
period # $ 4
period 1:
period 2.:
period 3:
period 4:
period 5:
period 6:
period 7:
H, He
Be, F
Na, S
Ca, Ti, Cr, Co, Cu, As
Rb, Mo, Ag, Sr, Cd, Sn, I
Hg, Pb, Rn,Ce, Au, Cs, Ba
Fr, U
16.
Draw orbital diagrams to represent the ground state electron configurations of B, P and Fe.
17.
Distinguish between core and valence electrons.
18.
(a)
Define Hund’s rule of maximum multiplicity, the Pauli Exclusion Principle and the Aufbau
process, explaining how each affects the ground state electron configurations of the
elements.
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(b)
Indicate whether the following configurations of nitrogen represent a ground state, an
excited state or an impossible state. For each impossible or excited state, indicate which
rule or principle is violated.
1s
2s
2p
(i)
2s
2p
3s
(iii)
2s
2p
1s
2s
2p
1s
2s
2p
3s
(vi)
(v)
1s
2s
1s
2p
(c)
2s
2p
(viii)
(vii)
State 2 ways an electron configuration can violate the Pauli Exclusion Principle and thus
be an impossible state.
Identify
(a)
(b)
(c)
all 4th period elements with 3 unpaired electrons in the ground state.
all 2nd period elements with no unpaired electrons in the ground state.
the 4th period element with the most unpaired valence electrons in the ground state.
Indicate whether any of the following electron configurations cannot represent the ground state of
a neutral atom.
(a)
21.
2p
(iv)
1s
20.
2s
(ii)
1s
19.
1s
ls2 2s2 2p x1 2p y1 (b) [Ar] 3d4 4s2 (c) 1s2 2s1 2p 6 3p 1
The quantum numbers listed below are for four different electrons in the same atom. Arrange them
in order of increasing energy. Indicate whether any two have the same energy.
(a) n=4, l =0, ml = 0, ms=1/2 (b)
n=3 l =2, ml = 1, ms= 1/2
(c) n=3, l =2, ml = -2, ms=-1/2
(d)
n=3, l =1, ml =1, ms=-1/2
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22.
What is the maximum number of electrons in an atom that can have the following quantum
numbers?
(a)
(c)
23.
n=4, l=2
n=3
(b)
(d)
n=3, l=2, ml =!1, ms= !1/2
n=5, l=3, ml = !2
Identify the atom represented by the following electron configurations: (some are excited states)
(a) [Ar] 3d10 4s2 (b) 1s22s12p 2 (c) [Xe] 4f145d 10 6s2 6p 2 (d) ls 22s22p 63s23p 63d 1 (e) [Ar]3d104s1
Note: Read pages 335 and 336(8th Edition) or 314!316(9th Edition) to answer questions 24, 25 and
26.
24.
Distinguish between radial probability density R2(r) and radial probability distribution
4Br2 R2(r) for a given orbital.
25.
Explain the fact that the radial probability density for a 1s orbital predicts that the maximum
probability for a 1s electron is at the nucleus but the electron is most likely to be found 53 pm from
the nucleus.
26.
Explain the fact that even though the most probability distance of a 2p electron is closer to the
nucleus than that of a 2s electron, the effective nuclear charge Zeff of the 2p electron is lower and
its energy is higher.
27.
In the seventh period, what would be the atomic number and electron configuration of the element
that
(a)
completes the 6d subshell
(b)
completes the period.
28.
Identify which block of the periodic table the following belong to: the halogens, the alkaline earth
metals, the transition metals, the lanthanides.
29.
How many valence electrons do each of the following atoms have, S, K, Fe, B, Ar, Pb? What is
the valence electron configuration of each atom?
30.
(a)
(b)
Determine the total number of nodes and the number of radial and angular nodes for the
following orbitals: 7s, 4p, 6d, 5f.
What is the difference between radial and angular nodes?
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31.
n2 h2
This question deals with a particle in a one dimensional box with E(n) =
.
8 mL2
(a)
(b)
(c)
What happens to the energy levels as the length of the box increases?
Calculate the zero!point energy of an electron (me = 9.109 x 10 G31 kg) in a one
dimensional box of length L = 100.0 nm.
Sketch an energy level diagram to show the relative energies of the first three energy levels.
Answers:
1.
frequency (<) the # waves passing a fixed point in one second
wavelength (8) the length of one complete cycle
velocity how fast the wave moves, i.e. the speed of light (c).
intensity the density of waves in a particular region of space.
2(a)
(b)
(c)
3(b)
(c)
(d)
4(a)
(b)
5.416 x 1014 Hz
3.589 x 10-19 J
216.1 kJ molG1
5.07 x 10G19 J
392 nm
yes
8.21 x 10G19 J
494 kJ molG1
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4 pathways with 1, 2, 2 and 3 photons emitted.
n=4
n=3
n=2
n=1
pathway one
(3 photons)
pathway two
(2 photons)
pathway three
(2 photons)
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pathway four
(one photon)
6.
(a) (i) absorbed (ii) E = 4.576 x 10G19 J, < = 6.906 x 1014 sG1 8 = 434.1 nm
(b) n = 7
7.
(a) n = 15 energy level is allowed (b) n = 4.34 energy level (orbit) does not exist.
8.
E(l) = !1.961 x 10G17 J (more negative i.e. lower value than H atom)
r(l) = 5.9 pm (orbit is closer to nucleus than corresponding orbit of H atom)
9. (a) threshold frequency (<o) the frequency of light which has just enough energy to eject an electron
from a metal surface in the photoelectric effect.
work function (threshold energy) (h<o) the minimum energy required to eject an electron from a
metal surface in the photoelectric effect.
(b) A single photon can eject only one electron. The higher the intensity of light, the greater the number
of photons striking the metal surface and the greater the number of electrons ejected. The kinetic
energy of the ejected electrons depends on the energy of the photon in excess of the threshold
energy. Photon energy and hence the excess energy available to the ejected electron, is directly
proportional to the frequency of the photon.
10.(a)
(c)
principal: describes orbital size which increases with value of n2. It also
indicates the shell it belongs to.
orbital angular momentum: describes orbital shape
magnetic: describes orbital orientation in x, y, z cartesian coordinate system centered at
nucleus
(i)
five 3d's (ii) one 5s (iii) seven 7f's (iv) three 2p's
(i)
3 orbitals, each has n=3 and l =1, and one of the ml values, +1, 0, or !1.
(ii)
1 orbital with n=4, l=0, and ml = 0.
(iii)
5 orbitals, each with n=5 and l =2 and one of the ml values, +2, +1, 0, !1, or !2.
(iv)
7 orbitals, each with n=6, l=3, and one of the ml values, +3, +2, +1, 0, !1, !2,
or !3.
11.
(3, 1, +2, +½) ml cannot be +2 if l = 1
(5, 4, !4 +1) ms cannot be +1, only +½ or !½
(2,2, 0, !½) l cannot be 2. For n = 2, l can only be 0, 1
(0,1, +1, +½) n cannot be 0. Smallest value of n is one.
12.
3 is value of n i.e. shell number, p is the code for l = 1, z means orbital oriented along imaginary
z axis centered at nucleus, 2 means 2 electrons in orbital.
13.
(a) 2s is larger than 1s (b) Both orbitals have same size, shape and energy but have different spatial
orientations.
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14.
(a)
(b)
electron #1: n=1, l=0, ml =0, ms=½
electron #2: n=1, l =0, ml=0, ms=!½
electron #3: n=2, l=0, ml =0, ms=½ or !½
a 4p electron must have n=4 and l =1. It must have one of the ml values, +1, 0, or !1. It
can have either ms=+½ or ms=!½.
15.
H(Z=1) 1s1 He (Z = 2) ls 2
Be (Z = 4) 1s22s2 F (Z = 9) 1s22s22p 5
Na (Z = 11) 1s22s22p 63s1 S (Z = 16) 1s22s22p 63s23p 4
Ca (Z= 20) [Ar] 4s2 Ti (Z = 22) [Ar] 3d24s2 Sr (Z = 38) [Kr] 5s2
Cr (Z= 24) [Ar] 3d54s1 Co (Z = 27) [Ar] 3d74s2 Ba (Z = 56) [Xe] 6s2
Cu (Z = 29) [Ar] 3d104s1 As (Z = 33) [Ar] 3d104s24p 3 Ag (Z = 47) [Kr] 4d105s1
Rb (Z = 37) [Kr] 5s1 Cd (Z = 48) [Kr] 4d105s2 Mo (Z = 42) [Kr] 4d 55s1
Sn (Z = 50) [Kr] 4d105s25p 2 I (Z = 53) [Kr] 4d105s25p 5 Cs (Z = 55) [Xe] 6s1
Hg (Z = 80) [Xe] 4f145d 106s2 Pb (Z = 82) [Xe] 4f145d 106s26p 2
Rn (Z= 86) [Xe] 4f145d 106s26p 6 Ce (Z = 58) [Xe] 4f26s2
Fr (Z = 87) [Rn] 7s1 U (Z = 92) [Rn] 5f47s2 Au (Z = 79) [Xe] 4f145d 106s1
16.
1s
2s
1s
2s
1s
2s
2p
B (z = 5)
2p
3r
3p
P (z= 15)
2p
3s
3p
3d
4s
Fe (z = 26)
17.
Core electrons occupy shells and sub-shells close to nucleus. They are stable, low energy
electrons. Valence electrons occupy the shell of highest principal quantum number n. They are the
higher energy electrons of the atom and are found further from the nucleus than the core electrons.
They are most important in determining chemical properties.
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18.
19.
20.
21.
22.
23.
(a)
Aufbau Process: As protons are added one by one to the nucleus to build up the
elements, electrons are added to the available orbitals in order of increasing orbital energy,
filling each subshell completely before adding electrons to the next. Pauli Exclusion
Principle: no 2 electrons can have same four quantum numbers. Each orbital can be
occupied by a maximum of two electrons with opposite spins. Hund’s Rule of
Maximum Multiplicity: Electrons occupy the degenerate orbitals of a subshell singly all
with the same (parallel) spin to give the maximum multiplicity until forced to pair them up.
(b) either vii or viii can represent the ground state i, iii and vi are excited states which
disobey the Aufbau process. iv and v are excited states which disobey Hund’s rule. ii is
an impossible state as the Pauli Exclusion Principle cannot be disobeyed. The two
electrons in the 2s orbital cannot have the same spin. (c) PE Principle violated when two
electrons shown in an orbital have same spin or there is more than two electrons in an
orbital.
(a) V,Co,As (b) Be,Ne
(c) Cr
b and c
lowest energy: d<b=c<a :highest energy
(a) 10 (b) 1 (c) 18 (d) 2
(a) Zn (b) B (c) Pb (d) K (e) Cu
24.
For a given orbital, the radial probability density R2(r) gives the electron probability density at one
point at a distance r from the nucleus. The radial probability distribution gives the total probability
of finding the electron anywhere in an extremely thin shell of radius r from the nucleus. It is found
by multiplying the radial probability density R2(r) by the factor 4Br2, the area of the shell of radius
r.
25.
The radial probability distribution gives the total probability of finding the electron anywhere on a
thin shell of radius(r) from the nucleus and thickness (dr). At the nucleus, the volume of the shell
is so small that, even though the value of R(r) for the ls orbital is at a maximum, the radial
probability distribution (total probability of finding the electron) is essentially zero. At 53 pm, the
thin shell has a much larger volume and the total probability of finding the electron in that thin shell
reaches a maximum.
26.
As can be seen by comparing the radial probability distribution plots of the 2s and 2p orbitals in
Figure 9-32, there is a lower total probability of finding a 2p electron close to the nucleus (it has
lower penetration of the inner shell (ls electrons) and is more effectively screened from the nucleus.
The 2p electron feels a lower Zeff, is held less tightly by the nuclear charge, and has a higher energy
than a 2s electron.
27.
(a) Z = 112
28.
Halogens (p-block), alkaline earth metals (s-block), transition metals (d-block) and lanthanides (fblock).
EC: [Rn] 5f146d 107s2
(b)
Z = 118
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EC: [Rn] 5f146d 107s27p 6
29.
30.
31.
S: 3s23p 4(6eG), K: 4s1(1eG), Fe: 4s2(2eG), B: 2s22p 1(3eG), Ar: 3s23p 6(8eG), Pb: 6s26p 2(4eG).
(a)
orbital
# nodes (n-1)
# radial nodes
# angular nodes
7s
6
6
0
4p
3
2
1
6d
5
3
2
5f
4
1
3
(b)
Radial nodes (found in radial wave function) are spheres where R2 = 0. Angular nodes
(found in the angular wave function) are planes (or cones) where R2 = 0.
(a)
The levels crowd closer together.
(b)
E(ZPE) = 6.025 x 10G24 J
(c)
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Developed by Dr. Chris Flinn
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