Ch27_2
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1) A radioactive nucleus emits a
MeV
g
ray. What is the wavelength of the emitted photon (
sheet 22
) ? Indicate with a positive (negative) sign whether the wavelength of the photon is about equal to (much smaller than) the wavelength of an X-ray photon).
2) A hypothetical radioactive nucleus with nucleons undergoes
a
decay. What is the number of nucleons in the daughter nucleus (
sheet 21,26
) ? Indicate with a positive (negative) sign whether the daughter nucleus belongs to the same (a different) chemical element.
3) A hypothetical radioactive nucleus with protons undergoes
b-
decay. How many protons are in the daughter nucleus (
sheet 23
) ? Indicate with a positive (negative) sign whether there are 3 (2) particles in the final state including the daughter nucleus.
4) A hypothetical radioactive nucleus undergoes
b+
decay,
A
Z
X ->
A
(Z-1)
X' +
b+
+
n(
massless
)
(sheet 23)
. The mass difference between the initial nucleus and the final nucleus (computed with the atomic masses for the neutral atoms!) is atomic mass units
u
. Since in the difference [
m
(
A
Z
X)-
m
(
A
(Z-1)
X')] one electron too few has been subtracted, we must correct for this (see how this is done for the fusion reaction on
sheet 35p
). The neutrino gets maximum energy when the electron gets zero kinetic energy. Neglecting the kinetic energy of the daughter nucleus calculate the maximum neutrino energy in
MeV
(
sheet 27'
). Indicate with a positive (negative) sign whether the rest energy of the neutrino is nonzero (zero).
5) In the nuclear fission reaction n +
235
92
U = 2 light nuclei + 3 n ("n" stands for neutron and the 2 light nuclei have about the same number of nucleons)
MeV
of energy are released per fission. If it takes
Mev
per nucleon of input energy to dissolve the
235
92
U nucleus into all its constituents (nucleons), what is the binding energy per nucleon for the 2 light nuclei in
MeV
(
sheet 31,32,33
) ? Use 233 nucleons in order to account for the net 2 nucleons emitted in the reaction above and indicate with a positive (negative) sign whether the energy you calculate is input (released).
6) One of the nuclear fusion reactions powering the sun is
1
1
H +
1
1
H =
2
1
H + e
+
+
n
. What is the kinetic energy of the e
+
when the neutrino has an energy of
MeV
(
sheet 35,35'
) ? Neglect the kinetic energies of the hydrogen and deuterium nuclei. Use 1.007825
u
for
1
1
H, 2.014102
u
for
2
1
H, and 0.511
MeV
/c
2
for the electron rest energy. Indicate with a positive (negative) sign whether the temperatures needed to propel the two hydrogen nuclei together with enough kinetic energy that they overcome the repulsive Coulomb force is easy (difficult) to realize in the laboratory for bulk matter, i.e. not just for a few nuclei.
7) A
kg
laboratory worker spends 8 hrs each day at a distance of
m
from a
g
ray source which emits
MeV
in
g
rays at an activity of 10
8
s
-1
uniformly into all directions. Assume that 1/2 of the
g
ray energy is deposited in the worker, that the body exposes a 1.5
m
2
cross sectional area to the source, and that the "relative biological effectiveness (RBE)" is 1. In how many days has the worker accumulated the yearly allowed dose of 500
mrem
(
sheet 42
) ? (Hint: the worker intercepts the fraction {body area/surface area of a sphere with a radius equal to the source-worker distance} of the radiation. Get first the # of
J/kg/day
the worker absorbs, then convert this to
rem/day
using the definition of
a
rem
on
sheet 42
, and finally divide the
rem
allowed by the latter.) Indicate with a positive (negative) sign whether
a
,
b
and
g
radiation all have the same (different) relative biological effectiveness.
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