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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.
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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
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 Winter '08
 cramer
 Energy, Mass

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