38.1
NUCLEAR PHYSICS
EXERCISES
Section 38.1 Elements, Isotopes, and Nuclear Structure
13.
INTERPRET
This problem is about writing the conventional symbols for the isotopes of radon.
DEVELOP
The conventional symbol for a nucleus X is
Z
A
X, where
A
is the mass number and
Z
is the atomic
number.
EVALUATE
With the number of protons (
Z
=
86 for all radon isotopes) and neutrons
()
NAZ
=−
given, the mass
numbers of the three isotopes are, respectively,
AZN
=+= + =
86
125
211, 220, and 222. Therefore, the nuclear
symbols are
86
211
86
220
86
222
Ra
Ra, and
Ra.
,
ASSESS
Isotopes of a given element have the same number of protons (and hence
Z
) but different number of
neutrons (and hence
A
).
14.
Z
=
32 for germanium (a semiconductor under silicon in the periodic table) so this isotope has
=+=
32
44
76
+=
. Its symbol is
32
76
Ge.
15.
INTERPRET
This problem asks for a comparison of the number of nucleons and charges between two nuclei.
DEVELOP
The comparison can be made by noting that the conventional symbol for a nucleus X is
Z
A
X, where
A
is
the mass number and
Z
is the atomic number.
EVALUATE
(a)
The mass number (number of nucleons) is
A
=
35 for both.
(b)
The charge,
Ze
, of a potassium nucleus,
Z
=
19, is two electronic charge units greater than that for a chlorine
nucleus,
Z
=
17.
ASSESS
Equality in mass number
A
does not imply equality in atomic number
Z
. Two nuclei have the same
Z
only
when they are isotopes.
16.
The “radius” of the proton, implied by Equation 38.1, is12
.f
m
, while
a
0
52 9
=
.p
m is about44 10
4
.
×
times larger.
17.
INTERPRET
This problem is about the size of the fission products of
92
235
U.
DEVELOP
The nuclear radius can be estimated using Equation 38.1:
RR
A
A
==
0
13
12
//
(.
)
fm
EVALUATE
Two fission products as equal as possible would have
A
=
117 or 118, and radii of about
RA
=≈
)
.
59
fm.
/
ASSESS
Equation 38.1 is a good approximation for
R
since nucleons are packed tightly into the nucleus. The tight
packing also suggests that all nuclei have roughly the same density.
Section 38.2 Radioactivity
18.
INTERPRET
We determine the number of halflives until a radioactive sample decays to 10% of its initial activity.
This is a radioactive decay problem.
DEVELOP
We will use
NN
e
t
=
−
0
λ
with
=
010
0
.
and
=
ln
/
,
2
t
and solve for
t
in terms of
t
/
.
38
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Chapter 38
EVALUATE
NN
N
e
t
t
t
==
→
=
−
→
=
−
−
010
00
.l
n
(
.
)
ln( .
)
ln(
λ
2
332
12
)
.
//
tt
t
→=
ASSESS
Let’s see if that makes sense: after one halflife the activity is
1
2
the initial activity, after 2 it’s
1
4
, and after
3 it’s
1
8
.10% is just a bit less than
1
8
, so our answer of a little more than three halflives is about right.
19.
INTERPRET
In this problem we are asked to write down all possible betadecay processes for
29
64
Cu.
DEVELOP
Beta decay in
29
64
Cu can involve positronneutrino or electronantineutrino emission, or electron
capture.
EVALUATE
The reactions are:
29
64
29
64
40
Cu
Zn
Cu
Ni
30
64
28
64
→+
+
+
−
+
βν
(%
)
)
)
19
41
29
64
Cu
Ni
28
64
+→
+
−
e
ν
ASSESS
In each decay mode, charge and mass number are conserved.
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 Fall '10
 Pheong
 Nuclear Fission, Nuclear Fusion, Neutron, Nuclear physics

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