C
HAPTER
28
Quick Quizzes
1.
(b). The circumference of the orbit is
n
times the de Broglie wavelength
( )
2
rn
π
λ
=
, so
there are three times as many wavelengths in the
3
n
=
level as in the
level. Also, by
combining Equations 28.4, 28.6 and the defining equation for the de Broglie wavelength
1
n
=
( )
hmv
=
, one can show that the wavelength in the
3
n
=
level is three times as long.
2.
The quantum numbers associated with
orbital
states are
n
,
±
, and
m
±
. For a specified value
of
n
, the allowed values of
±
range from 0 to
n
– 1. For each value of
±
, there are (2
±
+ 1)
possible values of
m
±
.
(a) If
n
= 3, then
±
= 0, 1, or 2. The number of possible orbital states is then
()
[ ] ()
[ ]
20
1
21 1
22
1
1 3 5 9
++
+=++=
.
(b) If
n
= 4, one additional value of
±
is allowed (
±
= 3) so the number of possible orbital
states is now
( )
[ ]
92
31971
6
=
+
=
.
3.
(a) For
, there are 5 allowed values of
±
, namely
±
= 0, 1, 2, 3, and 4.
5
n
=
(b) Since
m
±
ranges from –
±
to +
±
in integer steps, the largest allowed value of
±
(
±
= 4 in
this case) permits the greatest range of values for
m
±
. For
5
n
=
, there are 9 possible
values for
m
±
: -4, -3, -2, –1, 0, +1, +2, +3, and +4.
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
nn
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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