Answer: E
1
−
E
4
=
Δ
E
=
−
2.18
×
10
−
18
J
(
1
n
2
f
−
1
n
2
i
)
=
−
2.18
×
10
−
18
J
(
1
1
2
−
1
4
2
)
=
−
2.18
×
10
−
18
J
(
15
16
)
=
−
2.04
×
10
−
18
J
After you obtain the energy, then you can realize that that energy has to correspond exactly to the energy of the photon that came in:
|
Δ
E
|
=
E
photon
=
h
ν
=
h
c
λ
where
h
is Planck's constant,
c
is the speed of light, and
λ
is the wavelength of the incoming photon. Thus, the wavelength is:
⇒
λ
=
h
c
E
photon
=
(
6.626
×
10
−
34
J
⋅
s
)
(
2.998
×
10
8
m/s
)
2.04
×
10
−
18
J
=
9.720
×
10
−
8
m
=
97.20 nm
Explanation:
