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Chemistry for Engineers
Homework1
Atomic Structure
Answer Key
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Hand in next Friday
13:00
Chemistry for Engineers
Homework 1: Atomic Structure
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Q1: Three lasers each emit monochromatic radiation of different wavelengths. Laser A’s radiation is found to have a frequency of 4.8 x 1014
Hz. Laser B emits photons of energy 386.4 kJ/mol. Laser C had a wavelength specification of 2.8 microns.
Useful constants:
Show calculation(s) to support your answer to the following:
R = 3.29 x 1015 Hz
h = 6.63 x 10-34 Js
c = 3 x 108 m/s
NA = 6.022 x 1023).
a) Which laser emits radiation of frequency 107 million million Hertz?
b) Which laser has a photon energy of 3.18 x 10-19 J?
c) Which laser emits a beam of visible light?
d) What is the energy of each photon emitted from laser C?
e) Which of the three lasers emits radiation of the shortest wavelength?
f) Which of the three lasers emits infrared photons?
(9 marks)
Q2: Consider the following nuclides: mercury-196, thallium-205,
osmium-189, iridium-193, lead-204 and gold-197
Q3: In each case, show your reasoning.
a) Which isotope has the lowest mass?
b) Which isotope has the most neutrons per nucleus?
c) Which isotope has the fewest protons per nucleus?
d) Which nuclide has the highest proportion of protons
per nucleus (as a percentage)?
a) Identify the doubly-charged cation ion containing 18 electrons and a
single nucleus that includes 24 neutrons
b) Identify the singly-charged anion ion containing 36 electrons and a
single nucleus that includes 46 neutrons?
c) Identify the metal with the electronic configuration [Ar]4s23d8
d) Written in the same style, what is the electron configuration of arsenic?
e) Written in the same style, what is the electron configuration of Mo 2+?
f) What doubly charged anion is isoelectronic with the caesium cation?
(as always, show calculations!)
Q4: a) How many orbitals would you expect to find in the
fourth electron shell (n = 4)?
b) What orbital is defined by the quantum numbers n = 5
and l = 1?
c) Which electrons experience a greater effective nuclear
charge (Zeff), the valence
electrons of Mg2+or those of Al3+? Explain.
Q5: Using the Rydberg equation: DE/h = c/l = n = R[(1/nL2 ) – (1/nU2 )]
for the atomic spectrum of hydrogen
a) Calculate the photon energy and wavelength corresponding to i) the three lowest
energy lines of the Balmer series and ii) the convergence limit of the Balmer series.
b) By calculating the wavelength of the highest energy line of the Paschen series,
determine if the two series of lines overlap
Q1: Three lasers each emit monochromatic radiation of different
wavelengths. Laser A’s radiation is found to have a frequency of
4.8 x 1014 Hz. Laser B emits photons of energy 386.4 kJ/mol.
Laser C had a wavelength specification of 2.8 microns.
E/h = c/l=n
a) Which laser emits radiation of frequency 107 million million
Hertz? Laser C n = c/l = 3 x 108 / 2.8 x 10-6
= 1.07 x 1014 s-1
b) Which laser has a photon energy of 3.18 x 10-19 J?
Laser A
E = hn
= 6.63 x10-34 x 4.8 x 1014
= 3.18 x10-19 J
c) Which laser emits a beam of visible light?
Laser A
l = c / n = 3 x 108 / 4.8 x 1014
= 6.25 x 10-7 m (625 nm)
(visible range is 400-800 nm)
d) What is the energy of each photon emitted from laser C (2 s.f.)?
E = hc / l
= 6.63 x 10-34 x 3 x 108 / 2.8 x 10-6
= 7.1 x 10-20 J
e) Which of the three lasers emits radiation of the shortest
wavelength?
3
Laser B Emol = 386.4 x 10 J/mol
E = Emol/NA= 6.416 x 10-19 J/photon
l = hc / E
= 6.63 x 10-34 x 3 x 108 / 6.416 x 10-19
= 3.1 x 10-7 m (or 310 nm)
(compare Laser A = 625 nm and Laser C = 2800 nm)
f) Which of the three lasers emits infrared photons?
Laser C
Q2: Consider the following nuclides: mercury-196, thallium-205,
osmium-189, iridium-193, lead-204 and gold-197
a) Which isotope has the lowest mass?
189Os
(189 Da)
b) Which isotope has the most neutrons per nucleus?
205Tl
(124 n)
c) Which isotope has the fewest protons per nucleus?
189Os
(76 p)
d) Which nuclide has the highest proportion of protons per nucleus
(as a percentage)? 196Hg (40.8%)
(2 + 2 + 2 + 3 marks)
Q3:
a) Identify the doubly-charged cation ion containing 18 electrons and
a single nucleus that includes 24 neutrons 44Ca2+
b) Identify the singly charged anion ion containing 36 electrons and a
single nucleus that includes 46 neutrons? 81 
Br
c) Identify the metal with the electronic configuration [Ar]4s23d8
nickel (Ni)
d) Written in the same style, what is the electron configuration of
arsenic? [Ar]4s23d104p3
e) Written in the same style, what is the electron configuration of
Mo2+? [Kr]4d4 (the s electrons are lost first, don’t forget!)
f) What doubly charged anion is isoelectronic with the caesium
cation? Te2- (both are [Xe])
(2 + 2 + 2 + 3 marks)
Q4:
a) How many orbitals would you expect to find in the fourth electron
shell (n = 4)?
16 ( = 42 ; one 4s, three 4p, five 4d, seven 4f)
b) What orbital is defined by the quantum numbers n = 5 and l = 1?
5p orbital
c) Which electrons experience a greater effective nuclear charge (Zeff),
the valence electrons of Mg2+ or those of Al3+? Explain.
Al3+ because the shielding is the same but the
nuclear charge is greater
than that of Mg2+ (13 protons instead of 12)
Q5:
a) Calculate the photon energy and wavelength corresponding to i) the
three lowest energy lines of the Balmer series and ii) the convergence
limit of the Balmer series.
Lowest energy line: nL = 2, nU = 3 so [(1/nL2 ) – (1/nU2 )] = 0.1389
DE = 3.03 x 10-19 J
l = 656.5 nm
second lowest energy line: nL = 2, nU = 4 so [(1/nL2 ) – (1/nU2 )] = 0.1875
DE = 4.09 x 10-19 J
l = 486.3 nm
third lowest energy line: nL = 2, nU = 5 so [(1/nL2 ) – (1/nU2 )] = 0.210
DE = 4.581 x 10-19 J
l = 434.2 nm
ii) the convergence limit: nL = 2, nU =  so [(1/nL2 ) – (1/nU2 )] = 0.25
DE = 5.453 x 10-19 J
l = 364.7 nm
Q5:
b) By calculating the wavelength of the highest energy line of the
Paschen series, determine if the two series of lines overlap
Highest energy Paschen line corresponds to electron falling from infinity
down to n = 3 state (i.e. convergence limit of Paschen series)
nL = 3, nU =  so [(1/nL2 ) – (1/nU2 )] = 0.1111
DE = 2.4236 x 10-19 J
l = 820.7 nm
 no overlap between Balmer (< 656 nm) and Paschen (> 821 nm) series