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Lecture 2
Atomic Theory II
Tutorial
1) A photon travels with a frequency of 8.57 x 1014 Hz.
a. Find the wavelength of this photon in nm?
c = λν
c
λ =
ν
3 × 1 0 8 m /s
8.5 7 × 10 1 4 s − 1
λ = 3 .5 0 × 1 0 − 7 m
λ =
λ = 3 .5 0 × 1 0 2 n m
b. Find the energy contained by a single photon. Put your answer in kJ.
E = hν
E = (6.63x10−34 Js) (8.57 x 1014 s −1 )
E = 5.68 x 10−19 J
E = 5.68 x 10−16 kJ
2) An electron drops from n = 5 to n = 3 in a hydrogen atom.
a. Find the energy contained by the photon that is released during this
transition.
−2.178 ×10−18 J
52
E5 = −8.712 × 10−20 J
E5 =
−2.178 × 10−18 J
32
E3 = −2.420 ×10−19 J
E3 =
ΔE = E3 − E5
ΔE = − 2.420 × 10−19 J − (−8.712 ×10−20 J)
ΔE = − 1.549 × 10−19 J
b. Find the frequency of the electromagnetic radiation that is released.
E = hν
ν=
E 1.549 ×10−19 J
=
= 2.34 × 1014 s −1
h 6.63 ×10−34 Js
c. At what speed does this electromagnetic radiation travel?
(3x108 m/s) The speed of electromagnetic waves (light) is a constant.
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d. What is the wavelength of this electromagnetic radiation?
c = λν
c
λ =
ν
3 .0 0 × 1 0 8 m /s
λ =
2 .3 4 × 1 0 1 4 s − 1
λ = 1 .2 8 × 1 0 − 6 m
λ = 1 .2 8 × 1 0 3 n m
3) An electron is traveling with a velocity of 3.92 x 106 m/s.
(mass e- = 9.11 x 10-31 kg)
a. What is its wavelength in nm?
λ=
h
6.63 ×10−34 Js
=
= 1.86 ×10−7 m = 1.86 ×102 nm
mv (9.11×10−34 kg)(3.92 × 106 m/s)
b. What is its frequency?
c = λν
c
ν =
λ
3 × 1 0 8 m /s
1 .8 6 × 1 0 -7 m
ν = 1 .6 1 × 1 0 1 5 s − 1
ν =
4) Find the momentum of an electron with a wavelength of 232 nm.
ρ = mv
λ=
h
h
=
mv ρ
ρ=
h
λ
=
6.63i10−34 Js
= 2.86 ×10−27 kg ⋅ m/s
−9
232i10 m
5) How many possible orientations exist in a p-sublevel?
The angular momentum quantum number (l) for a p-sublevel is 1. The magnetic
quantum numbers range from - l to + l . For a p-sublevel the magnetic quantum
numbers are -1, 0, and +1. Thus, there are THREE possible orientations in the
p-sublevel.
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6) What is the lowest principal quantum number that can have p-orbitals?
n-1 = l
n = l +1
n=1+1
n=2
7) If n=5:
a. What are the possible angular momentum numbers?
The angular momentum numbers range from 0 to n-1.
If n = 5 the possible angular momentum numbers are:
0, 1, 2, 3, and 4.
b. What do these numbers represent?
The angular momentum numbers represent the shape or type of orbital. 0 is an s-orbital,
1 is a p-orbital, 2 is a d-orbital, and 3 is an f-orbital.
8) If l = 3:
a. What are the possible magnetic quantum numbers?
-3, -2, -1, 0, 1, 2, and 3
b. What do these numbers represent?
These numbers define the orientation of the orbital in three-dimensional space. In this
case, there are seven different orientations (an f-sublevel).
9) What are the possible angular momentum, magnetic, and electron spin quantum
numbers associated with a single electron in the s-orbital of n = 2.
l = 0 (An s-orbital is defined by l = 0)
m = - l to + l , so m = 0 (there is only one orientation for an s-orbital)
ms= + ½ or – ½ (the one electron could be spin up or spin down.)
10) What are the possible angular momentum, magnetic, and electron spin quantum
numbers associated with a single electron in an f-orbital of n = 5.
l = 3 (l = 3 defines an f-orbital)
m = - l to + l , so m = -3, -2, -1, 0, +1, +2, or +3 (there are seven possible orientations
for f-orbitals)
ms= + ½ or – ½ (the one electron could be spin up or spin down.)
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