Chapter 21

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 substance that can be injected is (a) \(0.08\) (b) \(0.04\) (c) \(0.16\) (d) \(0.32\)

\({ }_{92} \mathrm{U}^{235}\) 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) \(9 \times 10^{9} \mathrm{ergs}\) (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) \(96 \mathrm{~g}\)

In natural radioactive disintegration, U-238 emits one \(\alpha\) and two \(\beta\) and then five \(\alpha\) particle successively. The end product obtained is (a) \({ }_{82} \mathrm{~Pb}^{218}\) (b) \({ }_{82} \mathrm{~Pb}^{214}\) (c) \({ }_{84} \mathrm{~Pb}^{218}\) (d) \({ }_{82} \mathrm{~Pb}^{216}\)

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

\({ }_{92} \mathrm{U}^{238}\) emits \(8 \alpha\) particles and \(6 \beta\) particle. The neutron/ 92 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

Half-life of radioactive \({ }^{14} \mathrm{C}\) is 5760 years. In how many years, \(200 \mathrm{mg}\) of \({ }^{14} \mathrm{C}\) will be reduced to \(25 \mathrm{mg}\) ? (a) 5760 years (b) 11520 years (c) 17280 years (d) 23040 years

One microgram of radioactive sodium \({ }_{11} \mathrm{Na}^{24}\) with a half- life of 15 hours was injected into a living system for a bio assay. How long will it take for the radioactivity to fall to \(25 \%\) of the initial value? (a) 60 hours (b) \(22.5\) hours (c) 375 hours (d) 30 hours

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) \(6 \mathrm{~g}\)

Observe the following statements regarding isotopes I. \(\mathrm{K}^{39}\) and \(\mathrm{Ca}^{40}\) are isotones II. Nuclides having different atomic number (Z) and mass number (a) but same number of neutrons (n) are called isotones. III. \(\mathrm{F}^{19}\) and \(\mathrm{Na}^{23}\) are isotones. The correct answer is (a) only I and II are correct (b) I, II and III are correct (c) only I and III are correct (d) only II and III are correct

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

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

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 \(\mathrm{t}_{1 / 2}=14 \mathrm{hr}, 10 \mathrm{~g}\) of the same substance will have a \(t_{1 / 2}\) equal to (a) 14 hours (b) 28 hours (c) 50 hours (d) 70 hours

The energy released during the fission of \(1 \mathrm{~kg}\) of uranium is (a) \(9.0 \times 10^{16} \mathrm{erg}\) (b) \(9 \times 10^{20} \mathrm{erg}\) (c) \(9.0 \times 10^{19} \mathrm{erg}\) (d) \(9 \times 10^{21} \mathrm{erg}\)

A radioactive element A decays by the sequence and with half-lives given below: \(\mathrm{A} \frac{\alpha}{30 \mathrm{~min}}>\mathrm{B} \frac{2 \beta}{2 \mathrm{days}} \rightarrow \mathrm{C}\) 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 \(A\). (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 1 1th hour starting with one \(\operatorname{mol} \mathrm{X}\) is (a) \((1 / 2)^{1 / 10}\) (b) \((1 / 2)^{11 / 10}\) (c) \((1 / 2)^{12 / 11}\) (d) \((1 / 2)^{1 / 11}\)

A radioactive element A decays by the sequence and with half-lives, given below A \((\) half-life \(=30 \min ) \stackrel{\mathrm{k}_{1}}{\longrightarrow} \mathrm{B}+\mathrm{a}\) \(\mathrm{B}\) (half-life \(=2\) days \() \stackrel{\mathrm{k}_{2}}{\longrightarrow} \mathrm{C}+2 \mathrm{~b}\) Which of the following statements is correct (a) \(\mathrm{B}\) and \(\mathrm{C}\) are isotopes (b) The mass number of \(\mathrm{B}\) is greater than \(\mathrm{A}\) (c) Atomic number of \(\mathrm{A}\) and \(\mathrm{C}\) are same (d) Disintegration constant \(\mathrm{k}_{2}>\mathrm{k}_{1}\)

A sample of radioactive substance gave 630 counts per minute and 610 counts per minute at times differing by hour. The decay constant \((\lambda)\) in \(\min ^{-1}\) is given by (a) \(\lambda=\frac{630}{610} \times 60\) (b) \(\mathrm{e}^{60 \mathrm{~A}}=\frac{630}{610}\) (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) \(40 \%\)

Match the following: List-I 1\. \(\mathrm{P}^{32}\) 2\. \(\mathrm{Na}^{24}\) 3\. \(\mathrm{Co}^{60}\) 4\. \(\mathrm{I}^{131}\) List-II (i) Location of the tumour in the brain (ii) Location of the blood clots and circulatory disorders (iii) Radiotherapy (iv) Agricultural research

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

Match the lists I and II and pick the correct matching from the codes given below: List-I A. isotope B. isobar C. isotone D. isosters E. isodiaphers List-sII (1) \({ }_{88} \mathrm{Ra}^{228}\) and \({ }_{89} \mathrm{Ac}^{228}\) (2) \({ }_{18} \mathrm{Ar}^{39}\) and \({ }_{19} \mathrm{~K}^{40}\) (3) \({ }_{1} \mathrm{H}^{2}\) and \({ }_{1} \mathrm{H}^{3}\) (4) \({ }_{92} \mathrm{U}^{235}\) and \({ }_{90}^{\mathrm{Th} 231}\) (5) \(\mathrm{CO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}\) The correct matching is: (a) \(\mathrm{A}-2, \mathrm{~B}-1, \mathrm{C}-4, \mathrm{D}-5, \mathrm{E}-3\) (b) \(\mathrm{A}-2, \mathrm{~B}-5, \mathrm{C}-1, \mathrm{D}-4, \mathrm{E}-3\) (c) \(\mathrm{A}-3, \mathrm{~B}-1, \mathrm{C}-2, \mathrm{D}-5, \mathrm{E}-4\) (d) \(\mathrm{A}-5, \mathrm{~B}-4, \mathrm{C}-1, \mathrm{D}-2, \mathrm{E}-3\) (e) \(\mathrm{A}-5, \mathrm{~B}-3, \mathrm{C}-1, \mathrm{D}-2, \mathrm{E}-4\)

A sample of \(U^{238}\left(t_{1 / 2}=4.5 \times 10^{9}\right.\) yrs) ore is found containing \(23.8 \mathrm{~g} \mathrm{U}^{238}\) 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: \(\mathrm{n} / \mathrm{p}\) 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

Which of the following pairs are isodiapheric pairs? (a) \({ }_{29} \mathrm{Cu}^{65}\) and \({ }_{24} \mathrm{Cr}^{55}\) (b) \({ }_{29} \mathrm{Cu}^{65}\) and \({ }_{24} \mathrm{Cr}^{52}\) (c) \({ }_{92}^{2} \mathrm{U}^{235}\) and \({ }_{90}^{24} \mathrm{Th}^{231}\) (d) \({ }_{92} \mathrm{U}^{238}\) and \({ }_{90}^{24} \mathrm{Th}^{231}\)

Which relation is/are correct? (a) \(1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~Bq}\) (b) \(1 \mathrm{Ci}=2.8 \mathrm{v} 10^{4} \mathrm{Rd}\) (c) \(1 \mathrm{~Bq}=1 \mathrm{dps}\). (d) \(1 \mathrm{~Bq}=10^{6} \mathrm{Rd}\)