Elements of Modern Physics
364
14. The element
32
P decays into
32
S (m s ≈ 31.972072) mu including the mass
of electrons) by β
–
-emission. If the maximum kinetic energy of the
electron is 1.7 MeV, what is the mass of
32
P?
15. The element
7
Be decays by electron capture. If the masses of
7
Be and
7
Li are 7.016930 and 7.016004 mu respectively, what is the energy and
momentum of the recoil nucleus?
16. In the thorium series, the initial nucleus is
238
U and the final nucleus is
206
Pb. How many α particles are emitted by each uranium nucleus? How
many electrons are emitted by each nucleus? If the lifetime is 6.5 × 10
9
years, how much helium is released from 1 g of
238
U in 1 year? A mineral
sample contains
206
Pb and
238
U in the ratio of 1 to 4. Assuming that the
Pb is from the decay of U, estimate the age of the sample.
17. For the reaction
6
Li + n →
3
H +
4
He with thermal neutrons, determine
the kinetic energy of
4
He. It is given that the Q value for the reaction is
4.78 MeV.
18. A beam of neutrons is incident on a piece of gold. Show that the intensity
of the beam as a function of the depth t of penetration is given by
I(t) = I(0) exp (– σnt) where σ is the capture cross-section and n is the
number of target nuclei per volume. If the emerging intersity is 74% of
the original intensity for t = 0.05 cm, what is the capture cross-section of
gold?
19. If an average energy of 200 MeV is released in the fission of each
235
U
nucleus, how mush
235
U is used in one day in a reactor operating at a
power of 50 MW?
20. There is evidence to believe the sum has been in the present stable
condition for the last 5 × 10
9
years. Assuming that the stable condition
implies that the change in the composition is less than 10%, argue that
nuclear fusion is the only feasible source of energy and that the sun is
likely to remain in the present condition for another 5 × 10
9
years. The
sun radiates an energy of about 4 × 10
26
J/s, and its mass is about
2 × 10
30
kg.
364
14. The element
32
P decays into
32
S (m s ≈ 31.972072) mu including the mass
of electrons) by β
–
-emission. If the maximum kinetic energy of the
electron is 1.7 MeV, what is the mass of
32
P?
15. The element
7
Be decays by electron capture. If the masses of
7
Be and
7
Li are 7.016930 and 7.016004 mu respectively, what is the energy and
momentum of the recoil nucleus?
16. In the thorium series, the initial nucleus is
238
U and the final nucleus is
206
Pb. How many α particles are emitted by each uranium nucleus? How
many electrons are emitted by each nucleus? If the lifetime is 6.5 × 10
9
years, how much helium is released from 1 g of
238
U in 1 year? A mineral
sample contains
206
Pb and
238
U in the ratio of 1 to 4. Assuming that the
Pb is from the decay of U, estimate the age of the sample.
17. For the reaction
6
Li + n →
3
H +
4
He with thermal neutrons, determine
the kinetic energy of
4
He. It is given that the Q value for the reaction is
4.78 MeV.
18. A beam of neutrons is incident on a piece of gold. Show that the intensity
of the beam as a function of the depth t of penetration is given by
I(t) = I(0) exp (– σnt) where σ is the capture cross-section and n is the
number of target nuclei per volume. If the emerging intersity is 74% of
the original intensity for t = 0.05 cm, what is the capture cross-section of
gold?
19. If an average energy of 200 MeV is released in the fission of each
235
U
nucleus, how mush
235
U is used in one day in a reactor operating at a
power of 50 MW?
20. There is evidence to believe the sum has been in the present stable
condition for the last 5 × 10
9
years. Assuming that the stable condition
implies that the change in the composition is less than 10%, argue that
nuclear fusion is the only feasible source of energy and that the sun is
likely to remain in the present condition for another 5 × 10
9
years. The
sun radiates an energy of about 4 × 10
26
J/s, and its mass is about
2 × 10
30
kg.