7.2 Problems 393
7.98 Natural Uranium, as found on earth, consists of two isotopes in the ratio
of^23592 U/^23892 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:^23892 U= 6. 52 × 109 years,^23592 U= 1. 02 × 109 years]
[University of Cambridge, Tripos 2004]7.99 Calculate the activity (in Ci) of 2. 0 μgof^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 1.0cm^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 twoα-emitting nuclei, with the same mass number, one withZ=84 and
the other withZ=82 had the same decay constant, and if the first emitted
α-particles of energy 5.3 MeV, estimate the energy ofα-particles emitted by
the second.
[Osmania University]
7.103 Calculate the energy to be imparted to anα-particle to force it into the
nucleus of^23892 U(r 0 = 1 .2fm)
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 theα-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 ofRaC′for which the
α-particle range at S.T.P is 6.97 cm assuming the Geiger Nuttal rule.
[Osmania University]
7.105 Theαparticles 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, JP, of the nuclear states are
given in brackets):-
(^14) O→ (^14) N∗+e++ν (0+→ 0 +)
(^6) He→ (^6) Li+e−+ν(0+→ 1 +)