This preview shows pages 1–3. Sign up to view the full content.
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.
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
ρ
=
M
/
V
. In this case
M
=
1
.66
×
1
0
27
A
kg and
V
= (4
π
/3)(
1
.5
×
1
0

1
5
)
3
A
m
3
. Thus
=
1
.
1
74
×
1
0
1
7
kg/m
3
=
1
.
1
74
×
1
0
1
4
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 40
1
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
) Use Equ. 40
1
(
b
) Evaluate
U
;
r
= 4.05 fm
R
2
=
1
.89 fm;
R
3
= 2.
1
6 fm
U
= (
1
.44 eV
.
nm)/(4.05
×
1
0
6
nm) = 0.356 MeV
9*
∙∙
(
a
) Calculate the radii of
56
1
4
1
Ba and
36
92
Kr from Equation 40
1
. (
b
) Assume that after the fission of
235
U into
1
4
1
Ba
and
92
Kr, the two nuclei are momentarily separated by a distance
r
equal to the sum of the radii found in (
a
), and
calculate the electrostatic potential energy for these two nuclei at this separation. (See Problem 8.) Compare your
result with the measured fission energy of
1
75 MeV.
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Virgil.E.Barnes
 Energy, Mass

Click to edit the document details