Use Equs. 3718 and 3715;
l
13.6
1240
=
n
1
n
1
2
2
2
1

Find integers
n
1
and
n
2
. Note
n
1
must be 1 in this case.
0.9375
=
n
1
n
1
2
2
2
1

n
1
= 1,
n
2
= 4. The transition is from
n
= 4 to
n
= 1.
68 ·
The wavelength of a spectral line of hydrogen is 1093.8 nm. Identify the transition that results in this line.
Proceed as in Problem 67
Find
n
1
and
n
2
by trial and error
1/
n
1
2
– 1/
n
2
2
= 0.0833
n
1
= 3,
n
2
= 6. The transition is from
n
= 6 to
n
= 3
69*·
Spectral lines of the following wavelengths are emitted by singly ionized helium: 164 nm, 230.6 nm, and
541 nm. Identify the transitions that result in these spectral lines.
1. Express
E
n
for He
+
; note that
Z
= 2
2. Use Equs. 3718 and 3715 to write
n
1
and
n
2
in
terms of
?
3. By trial and error identify the integers
n
1
and
n
2
for which
?
= 164 nm, 230.6 nm, and 541 nm.
E
n
= –(4
×
13.6/
n
2
) eV = –54.4/
n
2
eV
l
54.4
1240
=
n
1
n
1
2
2
2
1

For
?
= 164 nm,
n
2
= 3,
n
1
= 2; for
?
= 230.6 nm,
n
2
= 9,
n
1
= 3; for
?
= 541 nm,
n
2
= 7,
n
1
= 4
70 ··
We are often interested in finding the quantity
ke
2
/
r
in electron volts when
r
is given in nanometers. Show
that
ke
2
= 1.44 eV
⋅
nm.
From Equ. 3716 we have
ke
2
/
a
0
= 27.2 eV, where
a
0
= 0.0529 nm. So
ke
2
= 1.44 eV
.
nm.
71 ··
The wavelengths of the photons emitted by potassium corresponding to transitions from the 4P
3/2
and 4P
1/2
states to the ground state are 766.41 nm and 769.90 nm. (
a
) Calculate the energies of these photons in electron
volts. (
b
) The difference in the energies of these photons equals the difference in energy
?
E
between the 4P
3/2
and 4P
1/2
states in potassium. Calculate
?
E
. (
c
) Estimate the magnetic field that the 4p
electron in potassium
experiences.
(
a
)
hf
= (1240/
?
) eV;
?
in nm
hf
= 1.6179 eV for
?
=766.41 nm;
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