Astronomy C10 / L&S C70U: Fall 2010
Homework #2 Solutions
Maximum points possible = 50
1.
Absorption of Photons by Atoms
(11 points total).
(a) (2 points.)
Which transition has the same energy as
#1
→
#2
?
Jumping from state #1 to #2 is a jump of 5 of our energy units. There are two
other such jumps. One is from state #2 to #5, the other is from state #5 to
#7. [Graders: Either one OK for full credit.]
(b) (3 points.)
What is the ratio of energies of the photons emitted by a pair of
downward jumps?
Jumping from state #6
→
#4 is a change of (13

9) = 4 units. Jumping from
#4
→
#3 is a change of (9

7) = 2 units. The ratio of energies is thus
2:1.
[Graders: 1/2 is also valid if the student flips the ratio.]
(c) (3 points.)
Can the photon emitted by
3
→
2
be absorbed by an atom with
electron in state 4?
The jump from #3
→
#2 emits a photon with (7

5) = 2 energy units. Looking
at the energy levels surrounding state #4, we see that jumping up to state #5
would take (10

9) = 1 unit, and a jump to state #6 would require (13

9) =
4 units.
Absorption can only occur when the incoming photon has
exactly
the same
energy that one of the electron’s possible energy level jumps requires. No “par
tial” absorption is possible. The emitted photon with 2 energy units is thus the
wrong size for the #4
→
#5 jump and is too weak to be considered for any of
the greater leaps.
This photon will NOT be absorbed.
(d) (3 points.)
If the jump from state
#2
→
#3
requires a photon with wavelength
5000
˚
A, what is the wavelength needed for the
#2
→
#4
jump?
The energy associated with the jump from #2
→
#3 is (7

5) = 2 units. The
jump from #2
→
#4 is (9

5) = 4 units. Thus, the larger jump will require
(4
/
2) = 2 times the energy.
The
energy
of a photon is directly proportional to its frequency. (
E
=
hν,
where
h
is “Planck’s constant” – Class Slide 25) However, the
wavelength
of a photon
is inversely proportional to its frequency (recall wavelength times frequency =
speed, so
ν
=
c/λ
). This means that energy is likewise inversely proportional to
wavelength:
E
=
hc/λ
.
A photon with 2 times the energy of another thus has 1/2 the wavelength. In
our case, the more energetic photon will then have a wavelength of
2500
˚
A.
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 Fall '10
 FILIPPENKO
 Energy, Photon, Wavelength, Class slide, Star Rachel

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