Problem 47
Actinium series starts with \(\mathrm{A}\) and ends at Z. \(\mathrm{A}\) and \(\mathrm{Z}\) are (a) \({ }_{90} \mathrm{Th}^{232},{ }_{82} \mathrm{~Pb}^{206}\) (b) \({ }_{90} \mathrm{Th}^{235},{ }_{82} \mathrm{~Pb}^{207}\) (c) \({ }_{92} \mathrm{U}^{235},{ }_{82} \mathrm{~Pb}^{207}\) (d) \({ }_{90} \mathrm{Ac}^{227},{ }_{82} \mathrm{~B} \mathrm{i}^{209}\)
Problem 48
Bismuth is the end product of radioactive disintegration series known as (a) \(4 n\) (b) \(4 n+1\) (c) \(4 n+2\) (d) \(4 n+3\)
Problem 49
The end product of \((4 n+2)\) disintegration series the (a) \({ }_{82} \mathrm{~Pb}^{204}\) (b) \({ }_{82} \mathrm{~Pb}^{208}\) (c) \({ }_{82} \mathrm{~Pb}^{209}\) (d) \({ }_{82} \mathrm{~Pb}^{206}\)
Problem 50
Consider the following process of decay, \({ }_{92} \mathrm{U}^{234} \rightarrow{ }_{90} \mathrm{Th}^{230}+{ }_{2} \mathrm{He}^{4} ; t_{1 / 2}=2,50,000\) years \({ }_{90} \mathrm{Th}^{230} \rightarrow{ }_{88} \mathrm{Ra}^{226}+{ }_{2} \mathrm{He}^{4} ; t_{1 / 2}=80,000\) years \({ }_{88} \mathrm{Ra}^{226} \rightarrow{ }_{86} \mathrm{Rn}^{222}+{ }_{2} \mathrm{He}^{4} ; t_{1 / 2}=1600\) years After the above process has occurred for a long time, a state is reached where for every two thorium atoms formed from \({ }_{92} \mathrm{U}^{234}\), one decomposes to form \({ }_{88} \mathrm{Ra}^{226}\) and for every two \({ }_{88} \mathrm{Ra}^{226}\) formed, one decomposes. The ratio of \({ }_{90} \mathrm{Th}^{230}\) to \({ }_{88} \mathrm{Ra}^{226}\) will be (a) \(250000 / 80000\) (b) \(80000 / 1600\) (c) \(250000 / 1600\) (d) \(251600 / 8\)
Problem 52
A radioactive isotope is being produced at a constant rate \(\mathrm{d} N / \mathrm{d} t=R\) in an experiment. The isotope has a half-life, \(t_{1 / 2}\). After a time \(t \gg t_{1 / 2}\), the number of active nuclei will become constant. The value of this constant is (a) \(R\) (b) \(\underline{1}\) (c) \(R / \lambda\) (d) \(\lambda / R\)
Problem 53
The \(t_{1 / 2}\) of \(\mathrm{Pb}^{212}\) is \(8.0 \mathrm{~h}\). It undergoes decay to its daughter (unstable) element \(\mathrm{Bi}^{212}\) of half-life \(60.0\) minute. The time at which daughter element will have maximum activity, is (a) \(205.7 \mathrm{~min}\) (b) \(3.429 \mathrm{~min}\) (c) \(60.0 \mathrm{~min}\) (d) \(67.5 \mathrm{~min}\)
Problem 54
A radionuclide 'A' decays simultaneously into 'B' and ' \(\mathrm{C}\) ', by \(\alpha\) - and \(\beta\) -emission, respectively. The half-lives for the decay are 20 and \(60 \mathrm{~min}\), respectively. The time in which \(87.5 \%\) of ' \(\mathrm{A}\) ' will decay is (a) \(15 \mathrm{~min}\) (b) \(30 \mathrm{~min}\) (c) \(45 \mathrm{~min}\) (d) \(60 \mathrm{~min}\)
Problem 56
The number of neutrons accompanying the formation of \({ }_{54} \mathrm{Xe}^{139}\) and \({ }_{38} \mathrm{Sr}^{94}\) from the absorption of slow neutron by \({ }_{92} \mathrm{U}^{235}\) by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3
Problem 57
Complete the following nuclear reaction: \({ }_{25} \mathrm{Mn}^{55}(n, \gamma)\) (a) \({ }_{25} \mathrm{Mn}^{55}\) (b) \({ }_{24} \mathrm{Cr}^{56}\) (c) \({ }_{24} \mathrm{Cr}^{54}\) (d) \({ }_{25} \mathrm{Mn}^{56}\)
Problem 58
In the reaction: \({ }_{4} \mathrm{Be}^{9}+\mathrm{X} \rightarrow{ }_{5} \mathrm{~B}^{10}+\gamma, \mathrm{X}\) is (a) proton (b) deuteron (c) \(\alpha\) -particle (d) neutron
