Download Quiz 4

CHEM 141-01
Fall 2006
Quiz # 4
Name_______________________________
Use the following values in the problems if needed:
c = 3.00 × 108 m/s (speed of light)
h = 6.63 × 10–34 J·s (Plank’s constant)
B = 2.18 × 10–18 J (Rydberg constant, a.k.a. RH)
1. (7 points) Find the frequency of light (in hertz, Hz) that has a wavelength of 566 nm.
566 nm = 566 × 10–9 m = 5.66 × 10–7 m
ν=
ν=
8
3.00 × 10 m / s
5.66 × 10
−7
m
c
λ
= 5.30 × 1014 / s = 5.30 × 1014 Hz
2. (8 points) A photon has a wavelength of 624 nm. Calculate the energy of the photon in
joules.
E = hν =
hc (6.63 × 10−34 J s)(3.00 × 108 m / s)
=
= 3.19 × 10−19 J
−
9
λ
624 × 10 m
3. (7 points) Calculate the frequency (in Hz) of a photon emitted by a hydrogen atom
when its electron drops from the n = 5 state to the n = 3 state.
In this problem ni = 5 and nf = 3.
⎛ 1
1
ΔE = RH ⎜
−
⎜n2
nf 2
⎝ i
⎞
⎛ 1
1 ⎞
⎟ = (2.18 × 10−18 J) ⎜
−
= − 1.55 × 10−19 J
2
2 ⎟
⎟
3 ⎠
⎝5
⎠
The sign of ΔE means that this is energy associated with an emission process.
Ephoton = hν and Ephoton = ΔEelectron
thus,
ΔEelectron = hν
and
ν=
ΔE
1.55 × 10−19 J
=
= 2.34 × 1014 s −1 = 2.34 × 1014 Hz
−34
6.63 ×10 J ⋅ s
h
4. (7 points) An electron in a certain atom is in the n = 2 quantum level. List the possible
values of l (and for each l list all values of ml ) that it can have.
The angular momentum quantum number l can have integral (i.e. whole number)
values from 0 to n − 1. In this case n = 2, so the allowed values of the angular
momentum quantum number are 0 and 1.
Each allowed value of the angular momentum quantum number labels a subshell.
Within a given subshell (label l) there are 2l + 1 allowed energy states (orbitals) each
labeled by a different value of the magnetic quantum number. The allowed values run
from −l through 0 to +l (whole numbers only). For the subshell labeled by the angular
momentum quantum number l = 1, the allowed values of the magnetic quantum number
are −1, 0, and 1. For the other subshell in this problem labeled by the angular momentum
quantum number l = 0, the allowed value of the magnetic quantum number is 0.