CHAPTER
40
Nuclear Physics
1*
·
Give the symbols for two other isotopes of (
a
)
14
N, (
b
)
56
Fe, and (
c
)
118
Sn
(
a
)
15
N,
16
N;
(
b
)
54
Fe,
55
Fe;
(
c
)
114
Sn,
116
Sn
2
·
Calculate the binding energy and the binding energy per nucleon from the masses given in Table 401 for
(
a
)
12
C, (
b
)
56
Fe, and (
c
)
238
U.
(
a
) Use Equ. 403 and Table 401.
(
b
), (
c
) Proceed as in part (
a
)
(
a
)
E
b
= (6
×
1.007825 + 6
×
1.008665  12.00)931.5 MeV =
92.16 MeV;
E
b
/
A
= 7.68 MeV
(
b
)
Z
= 26,
N
= 30;
E
b
= 488.1 MeV;
E
b
/
A
= 8.716 MeV
(
c
)
Z
= 92,
N
= 146;
E
b
= 1804 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
= 31.99 MeV;
E
b
/
A
= 5.33 MeV
(
b
)
Z
= 19,
N
= 20;
E
b
= 333.7 MeV;
E
b
/
A
= 8.556 MeV
(
c
)
Z
= 82,
N
= 126;
E
b
= 1636.5 MeV;
E
b
/
A
= 7.868 MeV
4
·
Use Equation 401 to compute the radii of the following nuclei: (
a
)
16
O, (
b
)
56
Fe, and (
c
)
197
Au.
(
a
), (
b
), (
c
) Use Equ. 401
(
a
)
R
16
= 3.78 fm; (
b
)
R
56
= 5.74 fm; (
c
)
R
197
= 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 401. (
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. 401,
R
=
R
0
A
1/3
, the nuclear volume is
V
= (4
p
/3)
R
0
3
A
. With
m
=
CA
,
r
=
m
/
V
= 3
C
/4
p
R
0
3
.
(
b
) Given that
C
= 1/6.02
×
10
23
g and
R
0
= 1.5
×
10
13
cm,
r
= 1.18
×
10
14
g/cm
3
.
6
·
Derive Equation 402; that is, show that the rest energy of one unified mass unit is 931.5 MeV.
1 u = 1.660540
×
10
27
kg (see p. EP4). Hence, u
c
2
= [(2.997924
×
10
8
)
2
×
1.660540
×
10
27
/1.602177
×
10
19
] eV =
9.3149
×
10
8
eV = 931.49 MeV.
7
·
Use Equation 401 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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentChapter 40
Nuclear Physics
The density of a sphere is
r
=
M
/
V
. In this case
M
= 1.66
×
10
27
A
kg and
V
= (4
p
/3)(1.5
×
10
15
)
3
A
m
3
. Thus
r
= 1.174
×
10
17
kg/m
3
= 1.174
×
10
14
g/cm
3
.
8
··
The electrostatic potential energy of two charges
q
1
and
q
2
separated by a distance
r
is
U
=
kq
1
q
2
/r, where
k
is
the Coulomb constant. (
a
) Use Equation 401 to calculate the radii of
2
H and
3
H. (
b
) Find the electrostatic potential
energy when these two nuclei are just touching, that is, when their centers are separated by the sum of their radii.
(
a
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 cramer
 Radioactive Decay, HalfLife, Energy, Mass, Nuclear Fission, Neutron, MeV

Click to edit the document details