Chapter 28
Atomic Physics
Quick Quizzes
1.
(b). The allowed energy levels in a one-electron atom may be expressed as
( )
2
13.6 eV
n
EZ
n
=−
2
, where
Z
is the atomic number. Thus, the ground state
( )
1 level
n
=
in helium, with
, is lower than the ground state in hydrogen, with
.
2
Z
=
1
Z
=
2.
(a). The energy of the photon emitted when the electron in a one-electron atom makes a
transition from a state having principal quantum number
to one having principal
quantum number
i
n
f
n
is
()
2
22
11
eV
fi
nn
γ
i
n
13.6
Thus, for given values of
and
f
n
2
, the energy of the photon emitted by a helium atom,
with
, is four times that of the photon emitted when an electron makes the
corresponding transition in a hydrogen atom, with
Z
Z
=
1
=
.
3.
(a)
For
n
, there are 5 allowed values of
A
, namely
A
= 0, 1, 2, 3, and 4.
5
=
(b)
Since
m
A
ranges from –
A
to +
A
in integer steps, the largest allowed value of
A
(
A
= 4 in
this case) permits the greatest range of values for
m
A
. For
5
n
=
, there are 9 possible
values for
m
A
: -4, -3, -2, –1, 0, +1, +2, +3, and +4.
(c)
For each value of
, there are
A
2
1
+
A
possible values of
. Thus, there is 1 distinct
pair with
A
; 3 distinct pairs possible with
m
A
0
=
1
=
A
; 5 distinct pairs with
; 7
distinct pairs with
; and 9 distinct pairs with
2
=
A
3
=
A
4
=
A
. This yields a total of 25
distinct pairs of
A
and
that are possible when
m
A
5
n
=
.
4.
(d). Krypton has a closed configuration consisting of filled
shells as
well as filled 4
s
and 4
p
subshells. The filled
=1, =2, and =3
n
3
n
=
shell (the next to outer shell in Krypton)
has a total of 18 electrons, 2 in the 3
s
subshell, 6 in the 3
p
subshell and 10 in the 3
d
subshell.
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