Chemistry for Engineers

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Chemistry for Engineers Homework1 Atomic
Structure Answer
Key

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Chemistry for Engineers Homework 1 Atomic
Structure


Hand in next Friday 1300
Q1 Three lasers each emit monochromatic
radiation of different wavelengths. Laser As
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. Show calculation(s) to support your
answer to the following 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? 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? 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)? (as always, show
calculations!)

Useful constants R 3.29 x 1015 Hz h 6.63 x
10-34 Js c 3 x 108 m/s NA 6.022 x 1023).
(9 marks)
Q3 In each case, show your reasoning. 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 Ar4s23d8 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
Mo2? f) What doubly charged anion is
isoelectronic with the caesium cation?
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 Mg2or 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
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Q1 Three lasers each emit monochromatic
radiation of different wavelengths. Laser As
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. 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?
E / h c / l n
Laser C
n c/l
3 x 108 / 2.8 x 10-6 1.07 x 1014 s-1
Laser A
E hn
6.63 x10-34 x 4.8 x 1014
3.18 x10-19 J
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)
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d) What is the energy of each photon emitted from
laser C (2 s.f.)? e) Which of the three lasers
emits radiation of the shortest
wavelength? f) Which of the three lasers
emits infrared photons?
E hc / l
6.63 x 10-34 x 3 x 108 / 2.8 x 10-6
7.1 x 10-20 J
Laser B
Emol 386.4 x 103 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)
Laser C
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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? 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)?
189Os (189 Da)
205Tl (124 n)
189Os (76 p)
196Hg (40.8)
(2 2 2 3 marks)
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Q3 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 Ar4s23d8 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 Mo2? f) What
doubly charged anion is isoelectronic with the
caesium cation?
44Ca2
81Br?
nickel (Ni)
Ar4s23d104p3
Kr4d4
(the s electrons are lost first, dont forget!)
Te2- (both are Xe)
(2 2 2 3 marks)
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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.
16 ( 42
one 4s, three 4p, five 4d, seven 4f)
5p orbital
Al3 because the shielding is the same but the
nuclear charge is greater than that of Mg2 (13
protons instead of 12)
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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

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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 (lt 656 nm)
and Paschen (gt 821 nm) series