Chapter 21

Two radioactive elements \(\mathrm{A}\) and \(\mathrm{B}\) have decay constant \(\lambda\) and \(10 \lambda\) respectively. If the decay begins with the same number of atoms of the \(\mathrm{n}\), the ratio of atoms of \(\mathrm{A}\) to those of \(\mathrm{B}\) after time \(1 / 9 \lambda\) will be (a) \(\mathrm{e}^{-3}\) (b) \(\mathrm{e}^{2}\) (c) \(\mathrm{e}\) (d) \(\mathrm{e}^{-1}\)

During a K-electron capture (a) X-rays are emitted (b) neutrous are emitted (c) \(\alpha\) particles are emitted (d) \(\gamma\) rays are emitted

\({ }_{7} \mathrm{~N}^{13}\) changes to \({ }_{6} \mathrm{C}^{13}\) by the emission of (a) proton (b) electron (c) neutron (d) positron

The half-life of a radioactive isotope is 3 hours. If the initial mass of the isotope was \(300 \mathrm{~g}\), the mass which remained undecayed in 18 hours would be (a) \(4.68 \mathrm{~g}\) (b) \(2.34 \mathrm{~g}\) (c) \(1.17 \mathrm{~g}\) (d) \(9.36 \mathrm{~g}\)

If a \(\mathrm{X}^{\mathrm{b}}\) species emits firstly a positron, then \(2 \alpha\) and \(2 \beta\) particles and in last \(1 \alpha\) particle is also emitted and finally converts to \(\mathrm{Y}^{\mathrm{d}}\) species, so the correct relation is (a) \(\mathrm{c}=\mathrm{a}-5, \mathrm{~d}=\mathrm{b}-12\) (b) \(\mathrm{c}=\mathrm{a}-5, \mathrm{~d}=\mathrm{b}-10\) (c) \(\mathrm{c}=\mathrm{a}-6, \mathrm{~d}=\mathrm{b}-0\) (d) \(\mathrm{c}=\mathrm{a}-4, \mathrm{~d}=\mathrm{b}-12\)

A human body required \(0.01 \mu\) activity of radioactive substance after 24 hours. Half-life of radioactive substane is 6 hours. Then injection of maximum activity of a radioactive suhstance that can he injected is (a) \(0.08\) (b) \(0.04\) (c) \(0.16\) (d) \(0.32\)

\({ }_{2} \mathrm{U}^{235}\) nucleus absorbs a neutron and disintegrates into \({ }_{54} \mathrm{Xe}^{139},{ }_{38} \mathrm{Sr}^{94}\) and \(\mathrm{x}\). What will be the product \(\mathrm{x} ?\) (a) 3 neturons (b) 2 neturons (c) \(\alpha\) particle (d) \(\beta\) particle

The radioactive isotope \({ }^{60} \mathrm{Co}_{27}\) which is used in the treatment of cancer can be made by (n, p) reaction. For this reaction, the target nucleus is (a) \({ }_{28} \mathrm{Ni}^{59}\) (b) \({ }_{27} \mathrm{Co}^{59}\) (c) \({ }_{28} \mathrm{Ni}^{60}\) (d) \({ }_{27} \mathrm{Co}^{60}\)

Energy equivalent of \(0.001 \mathrm{mg}\) is (a) \(9 \times 10^{7} \mathrm{ergs}\) (b) \(9 \times 10^{9}\) ergs (c) \(9 \times 10^{7} \mathrm{~J}\) (d) \(9 \times 10^{5} \mathrm{~J}\)

A radioactive substance having a half-life of 3 days was received in 12 days. It was found that there was only \(3 \mathrm{~g}\) of the isotope in the container. The initial weight of the isotope when packed was (a) \(12 \mathrm{~g}\) (b) \(24 \mathrm{~g}\) (c) \(48 \mathrm{~g}\) (d) \(96 \mathrm{~g}\)

The mass of helium atom of mass number 4 is \(4.0026\) amu, while that of neutron and proton is \(1.0087\) and \(1.0078\) respectively in the same scale. Hence, the nuclear binding per nucleon in the helium atom is (a) \(7.18 \mathrm{MeV}\) (b) \(6.18 \mathrm{MeV}\) (c) \(8.18 \mathrm{MeV}\) (d) \(9.18 \mathrm{MeV}\)

The nucleus resulting from \({ }_{92} \mathrm{U}^{238}\) after successive emission of two \(\alpha\) and four \(\beta\) particle is (a) \({ }_{90} \mathrm{Th}^{230}\) (b) \({ }_{92} \mathrm{U}^{230}\) (c) \({ }_{88} \mathrm{Ra}^{230}\) (d) \({ }_{94} \mathrm{Pu}^{230}\)

Decrease in atomic number is observed during. (a) \(\alpha\) emission (b) \(\beta\) emission (c) positron emission (d) electron capture Select the correct answer. (a) \(1,2,3\) (b) \(2,3,4\) (c) \(1,3,4\) (d) \(1,2,3,4\)

The number of neutrons accompanying the formation of \(_{54} \mathrm{Xe}^{139}\) and \({ }_{38} \mathrm{Sr}^{94}\) from the absorption of slow neutrons by \({ }_{92} \mathrm{U}^{235}\) followed by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3

\({ }_{92} \mathrm{U}^{2.58}\) emits \(8 \alpha\) particles and \(6 \beta\) particle. The neutron/ proton ratio in the product nucleus is (a) \(60 / 41\) (b) \(62 / 41\) (c) \(61 / 62\) (d) \(61 / 40\)

The disintegration constant of a radioactive isotope whose half-life is 3 hours is (a) \(1.57\) per hour (b) \(1.92\) per hour (c) \(1.04\) per hour (d) \(0.231\) per hour

The half-life of a radioactive element is 40 days. Calculate the average life. (a) \(5.76\) days (b) \(57.6\) days (c) 646 days (d) \(4.56\) days

The half-life of a radioactive nuclide is \(0.693\) minutes. The time (in minutes) required for the disintegration of this nuclide from 10 grams to one gram is ........ (a) 1 (b) \(0.693\) (c) \(6.93\) (d) \(2.303\)

The half-life period of radium is 1580 years. It remains \(1 / 16\) after how many years? (a) 1580 years (b) 3160 years (c) 4740 years (d) 6320 years

The radioisotope, tritium \(\left({ }_{3}^{1} \mathrm{H}\right)\) has a half- life of \(12.3\) years. If the initial amount of tritium is \(32 \mathrm{mg}\), how many milligrams of it would remain after \(49.2\) years? (a) \(4 \mathrm{mg}\) (b) \(8 \mathrm{mg}\) (c) \(1 \mathrm{mg}\) (d) \(2 \mathrm{mg}\)

A radioactive isotope decays at such a rate that after 192 minutes only \(1 / 16\) of the origin amount remains. The half-life of the radioactive isotope is (a) \(12 \mathrm{~min}\) (b) \(24 \mathrm{~min}\) (c) \(32 \mathrm{~min}\) (d) \(48 \mathrm{~min}\)

An artificial radioactive isotope has \(_{7} \mathrm{~N}^{14}\) after two successive \(\beta\) particle emissions. The number of neutrons in the parent nucleus must be (a) 14 (b) 9 (c) 7 (d) 5

A radioactive isotope has a half-life of 8 days. If today \(125 \mathrm{mg}\) is left over, what was its original weight 32 days earlier? (a) \(2 \mathrm{~g}\) (b) \(4 \mathrm{~g}\) (c) \(5 \mathrm{~g}\) (d) \(6 \mathrm{~g}\)

If a substance with half-life of 3 days is taken to another place in 12 days. What is the amount of substance left now? (a) \(1 / 8\) (b) \(1 / 32\) (c) \(1 / 4\) (d) \(1 / 16\)

A sample of \({ }_{19} \mathrm{~K}^{40}\) contains invariably \({ }_{18} \mathrm{Ar}^{40} .\) This is because \({ }_{19} \mathrm{~K}^{40}\) has tendency to undergo (a) \(\alpha\) decay (b) positronium decay (c) \(\beta\) decay (d) \(\gamma\) decay

The radioisotope of hydrogen has a half-life of \(12.33\) y. What is the age of an old bottle of wine, whose \({ }_{1} \mathrm{H}^{3}\) radiation is \(10 \%\) of that present in a new bottle of wine? (a) 41 years (b) \(123.3\) years (c) \(1.233\) years (d) 410 years

Lead is the final product formed by a series of changes in which the rate determining stage is the radioactive decay of uranium-238. This radioactive decay is a first order reaction with a half-life of \(4.5 \times 10^{9}\) years. What would be the age of a rock sample originally lead free, in which the molar proportion of uranium to lead is now \(1: 3\) ? (a) \(1.5 \times 10^{9}\) years (b) \(2.25 \times 10^{9}\) years (c) \(4.5 \times 10^{9}\) years (d) \(9.0 \times 10^{9}\) years

The number of neutrons accompanying the formation of \(_{34} \mathrm{Xe}^{139}\) and \(\mathrm{Sr}^{94}\) from the absorption of slow neutron by \({ }_{92} \mathrm{U}^{235}\) followed by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3

\({ }_{13} \mathrm{Al}^{27}\) is a stable isotope. \({ }_{13} \mathrm{Al}^{29}\) is expected to disintegrate by (a) \(\alpha\) emission (b) \(\beta\) emission (c) positron emission (d) proton emission

The half-life period of a radioactive element is 140 days. After 560 days, one gram of the element will reduce to (a) \(1 / 2 \mathrm{~g}\) (b) \(1 / 4 \mathrm{~g}\) (c) \(1 / 8 \mathrm{~g}\) (d) \(1 / 16 \mathrm{~g}\)

The radiations from a naturally occurring radioactive substance, as seen after deflection by a magnetic field in one direction, are (a) definitely beta rays (b) either alpha or beta rays (c) both alpha and beta rays (d) definitely alpha rays

The half-life of a radio-isotope is three hours. If the mass of the undecayed isotope at the end of 18 hours is \(3.125 \mathrm{~g}\), what was its mass initially? (a) \(300 \mathrm{~g}\) (b) \(200 \mathrm{~g}\) (c) \(180 \mathrm{~g}\) (d) \(400 \mathrm{~g}\)

If \(5 \mathrm{~g}\) of a radioactive substance has \(\mathrm{t}_{1 / \mathrm{s}}=14 \mathrm{hr}, 10 \mathrm{~g}\) of the same substance will have a \(\mathrm{t}_{1,}\) equal to (a) 14 hours (b) 28 hours (c) 50 hours (d) 70 hours

A radioactive element A decays by the sequence and with half-lives given below: \(\mathrm{A} \frac{\alpha}{30 \min }-\mathrm{B} \frac{2 \beta}{2 \text { days }} \rightarrow \mathrm{C}\) Which one of the following statement is correct? (a) after two hours, less than \(10 \%\) of the initial \(\mathrm{A}\) is left (b) maximum amount of B present at any time is less than \(50 \%\) of the initial amount of \(\mathrm{A}\). (c) stomic number of \(\mathrm{A}\) and \(\mathrm{C}\) are same (d) both (a) and (c) are correct

At radioactive equilibrium, the ratio between the atoms of two radioactive elements \(\mathrm{X}\) and \(\mathrm{Y}\) was found to be \(3.1 \times 10^{9}: 1\) respectively. If \(\mathrm{T}_{50}\) of the element \(\mathrm{X}\) is \(2 \times 10^{10}\) years, then \(\mathrm{T}_{50}\) of the element \(\mathrm{Y}\) is (a) \(6.45\) years (b) \(3.1 \times 10^{6}\) years (c) \(6.2 \times 10^{7}\) years (d) \(21 \times 10^{8}\) years

What weight of \(\mathrm{C}^{14}\) will have radioactivity one curie if \(\lambda\) (disintegration constant) is \(4.4 \times 10^{-12} \mathrm{sec}^{-1}\) ? (a) \(3.7 \times 10^{-6} \mathrm{~kg}\) (b) \(51 \times 10^{-3} \mathrm{~kg}\) (c) \(1.96 \times 10^{-4} \mathrm{~kg}\) (d) \(1.7 \times 10^{-6} \mathrm{~kg}\)

Half-life period of the radioactive element \(X\) is 10 hours. Amount of \(X\) left in the 11 th hour starting with one \(\mathrm{mol} \mathrm{X}\) is (a) \((1 / 2)^{1 / 10}\) (b) \((1 / 2)^{11 / 10}\) (c) \((1 / 2)^{12 / 11}\) (d) \((1 / 2)^{1 / 11}\)

A sample of radioactive substance gave 630 counts per minute and 610 counts per minute at times differing by 1 hour. The decay constant \((\lambda)\) in \(\min ^{-1}\) is given by (a) \(\lambda=\frac{630}{610} \times 60\) (b) \(\mathrm{e}^{60 \mathrm{k}}=\frac{630}{610}\) (c) \(\lambda=\frac{2.303}{60} \log \frac{610}{630}\) (d) \(\lambda=\frac{2.303}{60} \times \frac{630}{610}\)

In one type of mutual annihilation of an electron and a positron, three \(\gamma\)-ray photons are produced. If each photon has an energy of \(0.3407 \mathrm{MeV}\), what is the mass of the positron in amu? ( \(1 \mathrm{amu}=931.5 \mathrm{MeV}\) ) (a) \(7.986 \times 10^{-4}\) (b) \(5.486 \times 10^{-4}\) (c) \(16.86 \times 10^{4}\) (d) \(2.243 \times 10^{-4}\)

Assuming the age of the earth to be \(10^{10}\) years, what fraction of the original amount of \({ }_{92} \mathrm{U}^{238}\) is still in existence on earth \(\left(\mathrm{t}_{1 / 2}\right.\) of \({ }_{92} \mathrm{U}^{238}=4.51 \times 10^{9}\) years \()\) ? (a) \(10 \%\) (b) \(20 \%\) (c) \(30 \%\) (d) \(40 \%\)

In the nuclear reaction: \({ }_{3} \mathrm{Li}^{7}+{ }_{1} \mathrm{H}^{1} \longrightarrow 2{ }_{2} \mathrm{He}^{4}\) the mass loss is nearly \(0.02 \mathrm{amu}\). Hence, the energy released (in units of million \(\mathrm{kcal} / \mathrm{mol}\) ) in the process is approximately (a) 100 (b) 200 (c) 400 (d) 600

Match the following: List-I (Series) 1\. thorium 2\. naptunium 3\. actinium 4\. uranium List-II (Particles emitted) (i) \(8 \alpha, 5 \beta\) (ii) \(8 \alpha, 6 \beta\) (iii) \(6 \alpha, 4 \beta\) (iv) \(7 \alpha, 4 \beta\) The correct matching is: 1 2 3 4 (a) (iii) (i) (iv) (ii) (b) (i) (ii) (iv) (iii) (c) (iii) (i) (ii) (iv) (d) (ii) (i) (iv) (iii)

Match the following: List-I (Reactions) 1\. \({ }_{4} \mathrm{Be}^{9}+{ }_{2} \mathrm{He}^{4} \longrightarrow{ }_{6} \mathrm{C}^{12}+\ldots \ldots\) 2\. \({ }_{6} \mathrm{C}^{12}+\ldots \ldots \longrightarrow{ }_{5} \mathrm{~B}^{10}+{ }_{2} \mathrm{He}^{4}\) 3\. \({ }_{7} \mathrm{~N}^{14}+\ldots \ldots \longrightarrow{ }_{8} \mathrm{O}^{17}+{ }_{1} \mathrm{H}^{1}\) 4\. \({ }_{20} \mathrm{Ca}^{40}+\ldots \ldots \longrightarrow{ }_{19} \mathrm{~K}^{37}+{ }_{2} \mathrm{He}^{4}\) List-II (Particles) (i) \({ }_{2} \mathrm{He}^{4}\) (ii) \({ }_{0} \mathrm{n}^{1}\) (iii) \({ }_{1} \mathrm{D}^{2}\) (iv) \({ }_{1} \mathrm{H}^{1}\) The correct matching is: 1 2 3 4 (a) (ii) (i) (iii) (iv) (b) (iii) (ii) (i) (iv) (c) (i) (ii) (iv) (iii) (d) (ii) (iii) (i) (iv)

\({ }_{90} \mathrm{Th}^{232}\) decays to \({ }_{82} \mathrm{~Pb}^{206} .\) How many \(\alpha\) and \(\beta\) particles are emitted? (a) \(7 \alpha, 6 \beta\) (b) \(6 \alpha, 7 \beta\) (c) \(4 \alpha, 3 \beta\) (d) none of these

During the transformation of \(\mathrm{X}^{\mathrm{b}} \longrightarrow \mathrm{C}^{\mathrm{d}}\) the number of \(\beta\) particles emitted is (a) \(\frac{(b-d)}{4}\) (b) \((c-a)+1 / 2(b-d)\) (c) \((a-c)-1 / 2(b-d)\) (d) \((b-d)+2(c-a)\)

A sample of \(\mathrm{U}^{238}\left(\mathrm{t}_{1 / 2}=4.5 \times 10^{9} \mathrm{yrs}\right)\) ore is found con- taining \(23.8 \mathrm{~g} \mathrm{U}^{238}\) and \(20.6 \mathrm{~g}\) of \(\mathrm{Pb}^{206} .\) Calculate the age of the ore. (a) \(4.9 \times 10^{9}\) year (b) \(9.0 \times 10^{11}\) year (c) \(9.4 \times 10^{9}\) year (d) \(4.5 \times 10^{9}\) year

One of the hazards of nuclear explosion is the generation of \(\mathrm{Sr}^{90}\) and its subsequent incorporation in bones. This nuclide has a half life of \(28.1\) years. Suppose one microgram was absorbed by a new born child, how much \(\mathrm{Sr}^{90}\) will remain in his bones after 20 years? (a) \(61 \mu \mathrm{g}\) (b) \(61 \mathrm{~g}\) (c) \(0.61 \mu \mathrm{g}\) (d) none

Which of the following statement is/are correct? (a) The decay constant is independent of external factors like temperature and pressure (b) Nuclear isomers have same number of protons and neutrons (c) The decay constant is independent of the amount of the substance used (d) The value of decay constant generally decreases with the rise in temperature

Which is/are correctly matched? (a) Positron emission : \(\mathrm{n} / \mathrm{p}\) ration increases (b) \(\mathrm{K}\) - electron capture : \(\mathrm{n} / \mathrm{p}\) decreases (c) \(\beta\) - decay: n/p ration decreases (d) \(\alpha\) - decay: \(\mathrm{n} / \mathrm{p}\) ratio increases

Select the correct statements: (a) In the reaction \({ }_{11} \mathrm{Na}^{23}+\mathrm{Q} \rightarrow{ }_{12} \mathrm{Mg}^{23}+{ }_{0} \mathrm{n}^{1}\), the bombarding particle \(\mathrm{q}\) is deutron (b) In the reaction \({ }_{92} \mathrm{U}^{235}+{ }_{0} \mathrm{n}^{1} \rightarrow 56 \mathrm{Ba}^{140}+2\) \({ }_{0} \mathrm{n}^{1}+\mathrm{p}\), produced \(\mathrm{p}\) is \({ }_{36} \mathrm{Kr}^{94}\) (c) In a fission reaction, a loss in mass occurs releasing a huge amount of energy (d) A huge amount of energy is produced during nuclear fission and nuclear fussion reaction