392 7 Nuclear Physics – I
7.89 Determine the amount of^21084 Po necessary to provide a source ofα-particles
of 10 millicuries strength. Half life of Polonium=138 D.
7.90 A radioactive substance of half life 100 days which emitsβ-particles of aver-
age energy 5× 10 −^7 ergs is used to drive a thermoelectric cell. Assuming the
cell to have an efficiency 10%, calculate the amount (in gram-molecules) of
radioactive substance required to generate 5 W of electricity.
7.91 The radioactive isotope,^146 C does not occur naturally but it is found at con-
stant rate by the action of cosmic rays on the atmosphere. It is taken up by
plants and animals and deposited in the body structure along with natural
carbon, but this process stops at death. The charcoal from the fire pit of an
ancient camp has an activity due to^146 C of 12.9 disintegrations per minute,
per gram of carbon. If the percentage of^146 C compared with normal Carbon
in living trees is 1. 35 × 10 −^10 %, the decay constant is 3. 92 × 10 −^10 s−^1 and
the atomic weight=12.0, what is the age of the campsite?
[University of Liverpool]7.92 Consider the decay scheme RaEβ
→RaFβ
→RaG (stable). A freshly purified
sample of RaE weighs 5× 10 −^10 g at timet=0. If the sample is undisturbed,
calculate the time at which the greatest number of atoms of RaF will be
present and find this number. Derive any necessary formula [Half life of RaE(
210
83 Bi)
= 5 .0 days; Half life of RaF( 210
84 Po)
=138 days]
7.93 It is found that a solution containing 1 g of theα– emitter radium (^226 Ra)
never accumulates more than 6. 4 × 10 −^6 g of its daughter element radon
which has a half life of 3.825 days. Explain how the half life of radium may
be deduced from this information and calculate its value.
[University of London]
7.94 Find the mean-life of^55 Co radionuclide if its activity is known to decrease
4.0% per hour. The decay product is non-radioactive.
7.95 What proportion of^235 U was present in a rock formed 3, 000 × 106 years ago,
given that the present proportion of^235 Uto^238 U is 140?
[University of Liverpool]
7.96 A source consisting of 1μgof^242 Pu is spread thinly over one plate of an
ionization chamber. Alpha-particle pulses are observed at the rate of 80 per
second, and spontaneous fission pulses at the rate of 3 per hour. Calculate the
half life of^242 Pu and the partial decay constants for the two modes of decay.
[Osmania University]
7.97^90 Sr decays to^90 Ybyβdecay with a half-life of 28 years.^90 Y decays byβ
decay to^90 Zr with a half-life of 64 h. A pure sample of^90 Sr is allowed to
decay. What is the composition after (a) 1 h (b) after 10 years?
[University of Manchester]