Chem 1612007 Homework 9
th
Week
Hill & Petrucci Homework Chapter 7 & 8
Chapter 7 problems: 45,47,53,55,57,61,63,65,74,93
Chapter 8 problems: 3,21,25,27,31,37,75
The Bohr Model of the Hydrogen Atom
45.
What is the energy of the photon emitted when the electron in a hydrogen atom drops from the energy
level n=6 to the energy level (a) n = 1, and (b) n = 4?
∆E = B((1/n
f
2
) – (1/n
i
2
))
B = 2.179 x 10
18
J
(a) ∆E = (2.179 x 10
18
J)((1/(1)
2
) – (1/(6)
2
)) = 2.12 x 10
18
J; i.e., 2.12 x 10
18
J emitted.
(b) ∆E = (2.179 x 10
18
J)((1/(4)
2
) – (1/(6)
2
)) = 0.076 x 10
18
J; i.e., 0.076 x 10
18
J emitted.
47.
Calculate the frequency, in s
1
, of the electromagnetic radiation emitted by a hydrogen atom when its
electron drops from (a) the n = 5 to the n = 2 energy level, and (b) from the n = 3 to the n = 1 energy level.
∆E = B((1/n
f
2
) – (1/n
i
2
))
E
photon
= h υ
h υ = B((1/n
f
2
) – (1/n
i
2
))
υ = ((B)((1/n
f
2
) – (1/n
i
2
)))/(h)
(a) υ = ((2.179 x 10
18
J) x ((1/(2)
2
) – (1/(5)
2
)))/(6.626x10
34
Js) = 6.91 x 10
14
J
My answer to “a” is in disagreement with the Solutions Manual.
I don’t know why.
(b) υ = ((2.179 x 10
18
J) x ((1/(1)
2
) – (1/(3)
2
)))/(6.626x10
34
Js) = 29.2 x 10
14
J
Matter as Waves
53.
Calculate the wavelength, in nanometers, associated with a proton traveling at a speed of 1.96 x 10
5
ms
1
.
Use 1.67 x 10
27
kg as the proton mass.
DeBroglie theorem: λ= h/mv
λ= (6.626 x 10
34
Js)/((1.67 x 10
27
kg) x (1.96 x 10
5
ms
1
)) = 2.02 x 10
12
m
This answer is different than the Solutions Manual.
The Solutions Manual has a typo, calling the speed
1.96 x 10
6
ms
1
.
SelfAssessment Questions
55.
Electrons from an electron microscope have an associated wavelength of 0.00510 nm.
To what
speed, in meters per second, are the electrons accelerated?
λ= h/mv
v = h/λm
mass of one electron = 9.11 x 10
31
kg
v = (6.626 x 10
34
Js)/((0.00510 nm) x (1x10
9
m/nm) x (9.11 x 10
31
kg)) = 1.43 x 10
8
m/s
Quantum Numbers and Atomic Orbitals
Chem 1612007 homework 9
th
week
1
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57.
What is the lowest numbered principal shell in which (a) p orbitals are found, and (b) the f subshell
can be found?
From a graphical diagram, it can be seen that a p orbital is found in principal shells ≥2, and an f subshell
is found in principal shells ≥4.
61.
Indicate whether each of the following is a permissible set of quantum numbers.
If the set is not
permissible, state why it is not.
(a)
n
= 2,
l
= 0,
m
l
= +1
(b)
n
= 5,
l
= 3,
m
l
= 3
(c)
n
= 4,
l
= 3,
m
l
= 2
(d)
n
= 0,
l
= 0,
m
l
= 0
(a) If
n
= 2,
l
= 0 to 2 – 1 = 0 to 1.
Since
l
= 0, this is OK.
If
l
= 0,
m
l
= 0 to +0 = 0.
Since
m
l
= +1, this is not OK.
(b) If
n
= 5,
l
= 0 to 51 = 0,1,2,3 or 4.
Since
l
= 3, this is OK.
If
l
= 3,
m
l
= 3 to +3 = 3,2,1,0,+1,+2,+3.
Since
m
l
= 3, this is OK.
(c) If
n
= 4,
l
= 0 to 41 = 0 to 3 = 0,1,2 or 3.
Since
l
= 3, this is OK.
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 Fall '08
 vacillian
 Atom, Electron, Atomic orbital, Pauli exclusion principle

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