CHAPTER
37
Atoms
1* ·
As
n
increases, does the spacing of adjacent energy levels increase or decrease?
The spacing decreases.
2
·
The energy of the ground state of doubly ionized lithium (
Z
= 3) is ______ ,where
E
0
= 13.6 eV.
(
a
)
–9
E
0
, (
b
) –3
E
0
, (
c
)
–
E
0
/3,
(
d
)–
E
0
/9.
(
a
)
3
·
Bohr’s quantum condition on electron orbits requires
(
a
)
that the angular momentum of the electron about the hydrogen nucleus equal
nh
_
.
(
b
) that no more than one electron occupy a given stationary state.
(
c
) that the electrons spiral into the nucleus while radiating electromagnetic waves.
(
d
) that the energies of an electron in a hydrogen atom be equal to
nE
0
, where
E
0
is a constant energy and
n
is
an integer.
(
e
) none of the above.
(
a
)
4
··
If an electron moves to a larger orbit, does its total energy increase or decrease? Does its kinetic energy
increase or decrease?
Its total energy increases; its kinetic energy decreases.
5* ··
The kinetic energy of the electron in the ground state of hydrogen is 13.6 eV =
E
0
. The kinetic energy of the
electron in the state
n
= 2 is _____.
(
a
) 4
E
0
,
(
b
) 2
E
0
, (
c
)
E
0
/2,
(
d
)
E
0
/4.
(
d
)
6
·
The radius of the
n
= 1 orbit in the hydrogen atom is
a
0
= 0.053 nm.
What is the radius of the
n
= 5 orbit?
(
a
) 5
a
0
, (
b
) 25
a
0
, (
c
)
a
0
, (
d
) (1/5)
a
0
, (
e
) (1/25)
a
0
.
(
b
)
7
·
Use the known values of the constants in Equation 3711 to show that
a
0
is approximately 0.0529 nm.
Evaluate Equ. 3712,
a
0
=
h
_
2
/
mke
2
a
0
=
m
)
10
(1.6
10
8.99
10
9.11
)
10
(1.05
2
19
9
31
2
34



×
×
×
×
×
×
= 5.26
×
10
–11
m = 0.0526 nm
8
·
The longest wavelength of the Lyman series was calculated in Example 372. Find the wavelengths for the
transitions (
a
)
n
1
= 3 to
n
2
= 1 and (
b
)
n
1
= 4 to
n
2
= 1.
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