HW #8: Nuclear
Phys320 – Spring
2007
(Reshchikov)
p. 1
Homework # 8
Solutions
Problem 1
Compute the total binding energy B
(in MeV) and the binding energy per nucleon
B/A (in MeV/nucleon)
for the stable isotope
66
Zn (65.926037).
()
222
6
6
30
22
2
2
(
) (
)
where
30
and
66 30
36
for
Zn
30(1.007825 amu)
36(1.008665 amu)
(65.926037 amu)
(0.6207 amu)
0.6207 amu
931.5 MeV amu
578.2 MeV
578.2 MeV
66 nucle
HnA
BZ
M
cN
M
c
M
c
Z
N
Bc
cc
c
c
B
A
=+−
=
=
−
=
=
==
=
8.76 MeV/nucleon
ons
=
Problem 2
Compute the total binding energy B
(in MeV) and the binding energy per nucleon
B/A (in MeV/nucleon)
for unstable isotope
74
Zn (73.929460). Its halftime is 95.6 s.
7
4
30
2
2
(
) (
)
where
30
and
74 30
44
for
Zn
30(1.007825 amu)
44(1.008665 amu)
(73.929460 amu)
(0.68655 amu)
0.6866 amu
931.5 MeV amu
639.5 MeV
639.5 MeV
74 nucl
M
M
c
M
c
Z
N
c
c
B
A
=
=
−
=
=
=
8.642 MeV/nucleon
eons
=
Problem 3
The activity of a radioactive sample is initially 10
14
decays per second and it decreases to 10
10
decays per
second after 30 days. Find
τ
and t
1/2
of this radioactive element in any appropriate time units (s, min, h,
days,…, as you prefer). Also, find the initial number of radioactive nuclei in the sample.
( )
0
55
1/2
1
0
10
1
14
Solving for
in the decay equation R
R exp
gives:
30 days × 24 h/day
3.257 days = 78 h = 2.8 10
and
ln2
2.257 days = 54 h
1.95 10
10
ln
ln
10
Using the differential e
τ
t
t
τ
st
τ
s
R
s
R
s
τ
−
−
=−
=
×
=
=
=
×
⎛⎞
⎛
⎞
⎜⎟
⎝⎠
00
14
19
quation R
dN/dt =
N/ , the initial number of radioactive nuclei is given by:
3600 s
10 decays
N
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 Spring '04
 Baski
 Physics, Atom, Electron, Proton, Radioactive Decay, Energy, Work, Neutron, MeV

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