7.2 Problems
393
7.98 Natural Uranium, as found on earth, consists of two isotopes in the ratio
of
235
92 U/
238
92 U = 0.7%. Assuming that these two isotopes existed in equal
amounts at the time the earth was formed; calculate the age of the earth.
[Mean life times:
238
92 U = 6.52 × 10
9 years,
235
92 U = 1.02 × 10
9 years]
[University of Cambridge, Tripos 2004]
7.99 Calculate the activity (in Ci) of 2.0 μg of
224 ThX. ThX (T 1/2 = 3.64 D)
7.100 Calculate the energy in calories absorbed by a 20 kg boy who has received a
whole body dose of 40 rad.
7.101 A small volume of solution, which contained a radioactive isotope of sodium
had an activity of 16,000 disintegrations per minute/cm
3 when it was injected
into the blood stream of a patient. After 30 h, the activity of 1.0 cm
3 of the
blood was found to be 0.8 disintegrations per minute. If the half-life of the
sodium isotope is taken as 15 h, estimate the volume of the blood in the
patient.
7.2.10 Alpha-Decay
7.102 If two α-emitting nuclei, with the same mass number, one with Z = 84 and
the other with Z = 82 had the same decay constant, and if the first emitted
α-particles of energy 5.3 MeV, estimate the energy of α-particles emitted by
the second.
[Osmania University]
7.103 Calculate the energy to be imparted to an α-particle to force it into the
nucleus of
238
92 U (r 0 = 1.2 fm)
7.104 Radium, Polonium and RaC are all members of the same radioactive series.
Given that the range in air at S.T.P of the α-particles from Radium (half-life
time 1,622 Year) the range is 3.36 cm where as from polonium (half life time
138 D) the range is 3.85 cm. Calculate the half-life of RaC
for which the
α-particle range at S.T.P is 6.97 cm assuming the Geiger Nuttal rule.
[Osmania University]
7.105 The α particles emitted in the decays of 88 Ra
226 and 90 Th
226 have energies
4.9 MeV and 6.5 MeV, respectively. Ignoring the difference in their nuclear
radii, find the ratio of their half life times.
[Osmania University]
7.2.11 Beta-Decay
7.106 Classify the following transitions (the spin parity, J
P , of the nuclear states are
given in brackets):14 O →
14 N
∗
+ e
+
+ ν (0
+
→ 0
+ )
6 He →
6 Li + e
−
+ ν (0
+
→ 1
+ )
393
7.98 Natural Uranium, as found on earth, consists of two isotopes in the ratio
of
235
92 U/
238
92 U = 0.7%. Assuming that these two isotopes existed in equal
amounts at the time the earth was formed; calculate the age of the earth.
[Mean life times:
238
92 U = 6.52 × 10
9 years,
235
92 U = 1.02 × 10
9 years]
[University of Cambridge, Tripos 2004]
7.99 Calculate the activity (in Ci) of 2.0 μg of
224 ThX. ThX (T 1/2 = 3.64 D)
7.100 Calculate the energy in calories absorbed by a 20 kg boy who has received a
whole body dose of 40 rad.
7.101 A small volume of solution, which contained a radioactive isotope of sodium
had an activity of 16,000 disintegrations per minute/cm
3 when it was injected
into the blood stream of a patient. After 30 h, the activity of 1.0 cm
3 of the
blood was found to be 0.8 disintegrations per minute. If the half-life of the
sodium isotope is taken as 15 h, estimate the volume of the blood in the
patient.
7.2.10 Alpha-Decay
7.102 If two α-emitting nuclei, with the same mass number, one with Z = 84 and
the other with Z = 82 had the same decay constant, and if the first emitted
α-particles of energy 5.3 MeV, estimate the energy of α-particles emitted by
the second.
[Osmania University]
7.103 Calculate the energy to be imparted to an α-particle to force it into the
nucleus of
238
92 U (r 0 = 1.2 fm)
7.104 Radium, Polonium and RaC are all members of the same radioactive series.
Given that the range in air at S.T.P of the α-particles from Radium (half-life
time 1,622 Year) the range is 3.36 cm where as from polonium (half life time
138 D) the range is 3.85 cm. Calculate the half-life of RaC
for which the
α-particle range at S.T.P is 6.97 cm assuming the Geiger Nuttal rule.
[Osmania University]
7.105 The α particles emitted in the decays of 88 Ra
226 and 90 Th
226 have energies
4.9 MeV and 6.5 MeV, respectively. Ignoring the difference in their nuclear
radii, find the ratio of their half life times.
[Osmania University]
7.2.11 Beta-Decay
7.106 Classify the following transitions (the spin parity, J
P , of the nuclear states are
given in brackets):14 O →
14 N
∗
+ e
+
+ ν (0
+
→ 0
+ )
6 He →
6 Li + e
−
+ ν (0
+
→ 1
+ )