CHAPTER
40
Nuclear Physics
1*
∙
Give the symbols for two other isotopes of (
a
)
1
4
N, (
b
)
56
Fe, and (
c
)
11
8
Sn
(
a
)
1
5
N,
1
6
N;
(
b
)
54
Fe,
55
Fe;
(
c
)
11
4
Sn,
11
6
Sn
2
∙
Calculate the binding energy and the binding energy per nucleon from the masses given in Table 40
1
for
(
a
)
1
2
C, (
b
)
56
Fe, and (
c
)
238
U.
(
a
) Use Equ. 403 and Table 40
1
.
(
b
), (
c
) Proceed as in part (
a
)
(
a
)
E
b
= (6
×
1
.007825 + 6
×
1
.008665 
1
2.00)93
1
.5 MeV =
92.
1
6 MeV;
E
b
/
A
= 7.68 MeV
(
b
)
Z
= 26,
N
= 30;
E
b
= 488.
1
MeV;
E
b
/
A
= 8.7
1
6 MeV
(
c
)
Z
= 92,
N
=
1
46;
E
b
=
1
804 MeV;
E
b
/
A
= 7.58 MeV
3
∙
Repeat Problem 2 for (
a
)
6
Li, (
b
)
39
K, and (
c
)
208
Pb.
(
a
), (
b
), (
c
) Proceed as in Problem 402.
(
a
)
Z
= 3,
N
= 3;
E
b
= 3
1
.99 MeV;
E
b
/
A
= 5.33 MeV
(
b
)
Z
=
1
9,
N
= 20;
E
b
= 333.7 MeV;
E
b
/
A
= 8.556 MeV
(
c
)
Z
= 82,
N
=
1
26;
E
b
=
1
636.5 MeV;
E
b
/
A
= 7.868 MeV
4
∙
Use Equation 40
1
to compute the radii of the following nuclei: (
a
)
1
6
O, (
b
)
56
Fe, and (
c
)
1
97
Au.
(
a
), (
b
), (
c
) Use Equ. 40
1
(
a
)
R
1
6
= 3.78 fm; (
b
)
R
56
= 5.74 fm; (
c
)
R
1
97
= 8.73 fm
5*
∙
(
a
) Given that the mass of a nucleus of mass number
A
is approximately
m
=
CA
, where
C
is a constant, find an
expression for the nuclear density in terms of
C
and the constant
R
0
in Equation 40
1
. (
b
) Compute the value of this
nuclear density in grams per cubic centimeter using the fact that
C
has the approximate value of
1
g per Avogadro's
number of nucleons.
(
a
) From Equ. 40
1
,
R
=
R
0
A
1
/3
, the nuclear volume is
V
= (4
π
/3)
R
0
3
A
. With
m
=
CA
,
ρ
=
m
/
V
= 3
C
/4
R
0
3
.
(
b
) Given that
C
=
1
/6.02
×
1
0
23
g and
R
0
=
1
.5
×
1
0

1
3
cm,
=
1
.
1
8
×
1
0
1
4
g/cm
3
.
6
∙
Derive Equation 402; that is, show that the rest energy of one unified mass unit is 93
1
.5 MeV.
1
u =
1
.660540
×
1
0
27
kg (see p. EP4). Hence, u
c
2
= [(2.997924
×
1
0
8
)
2
×
1
.660540
×
1
0
27
/
1
.602
1
77
×
1
0

1
9
] eV =
9.3
1
49
×
1
0
8
eV = 93
1
.49 MeV.
7
∙
Use Equation 40
1
for the radius of a spherical nucleus and the approximation that the mass of a nucleus of mass
number
A
is
A
u to calculate the density of nuclear matter in grams per cubic centimeter.