Chapter 14

Which element has a relatively more stable nucleus? (a) U (b) \(\mathrm{H}\) (c) Fe (d) Ra

Which of the following is least likely to be stable? (a) \(\mathrm{Ca}^{40}\) (b) \(\mathrm{Al}^{30}\) (c) \(\mathrm{Sn}^{119}\) (d) \(\mathrm{Mn}^{55}\)

The energy required to separate the nucleons from a nucleus is called (a) nuclear energy (b) ionization energy (c) binding energy (d) lattice energy

The value of packing fraction of carbon-12 is (a) positive (b) negative (c) zero (d) infinite

Of the following isotopes, which one is likely to be the most stable? (a) \(\mathrm{Zn}^{63}\) (b) \(\mathrm{Zn}^{67}\) (c) \(\mathrm{Zn}^{71}\) (d) \(\mathrm{Zn}^{64}\)

The largest stable nucleus is (a) \(\mathrm{U}^{238}\) (b) \(\mathrm{B}_{1}^{209}\) (c) \(\mathrm{U}^{235}\) (d) \(\mathrm{Pb}^{206}\)

Among the isotopes of all the elements (only non-radioactive), the \(n / p\) ratio is maximum for (a) \(\mathrm{H}^{1}\) (b) \({ }_{1} \mathrm{H}^{3}\) (c) \({ }_{83} \mathrm{Bi}^{209}\) (d) \({ }_{2} \mathrm{He}^{4}\)

Among the isotopes of all the elements (radioactive as well as non- radioactive), the packing fraction is maximum for (a) \({ }_{1} \mathrm{H}^{1}\) (b) \({ }_{6} \mathrm{C}^{12}\) (c) \({ }_{1} \mathrm{H}^{3}\) (d) \({ }_{26} \mathrm{Fe}^{56}\)

\(\alpha\) -particle is considered identical to He-nucleus because (a) He-nucleus is present in the nuclei of all \(\alpha\) -emitters. (b) He-nucleus has two protons and two neutrons. (c) any sealed vessel containing some \(\alpha\) -emitter is found to contain He gas after some time. (d) He-nucleus is the most stable nucleus.

Emission of one \(\alpha\) -particle from a nucleus results the loss of two protons and two neutrons from the nucleus. These four particles (two protons and two neutrons) comes out from the nucleus (a) all at a time. (b) one by one, both protons followed by both neutrons. (c) one by one, both neutrons followed by both protons. (d) one by one, protons and neutrons alternatively.

In \(\beta\) -decay, an electron comes out from an atom. The electron comes out due to nuclear change, not from the orbit of the atom. It may be explained by the fact that on \(\beta\) -decay, (a) the atomic number increases by one unit. (b) the mass number remains unchanged. (c) the atomic species get changed. (d) the atomic species remains unchanged.

The isotope of \({ }_{90} \mathrm{Ra}^{231}\) can be converted to \({ }_{90} \mathrm{Th}^{227} \mathrm{by}\) (a) One alpha emission (b) Four beta emission (c) Two alpha and two beta emissions (d) One alpha and two beta emissions

When a nucleus reverts from an excited state to the ground state, the energy difference between the two states is emitted as (a) \(\alpha\) -particle (b) \(\beta\) -particle (c) \(\gamma\) -rays (d) neutrino

A free neutron decays to a proton but a free proton does not decay to a neutron. This is because (a) neutron is a composite particle made of a proton and an electron whereas proton is a fundamental particle (b) neutron is a uncharged particle whereas proton is a charged particle (c) neutron has larger rest mass than a proton (d) weak forces can operate in a neutron but not in a proton

A positron is emitted from \(\mathrm{Na}^{23}\) The ratio of the atomic mass and atomie number in the resulting nuclide is (a) \(\frac{22}{10}\) (b) \(\frac{22}{11}\) (c) \(\frac{23}{10}\) (d) \(\frac{23}{12}\)

Consider the beta decay, \(\mathrm{Au}^{198} \rightarrow \mathrm{Hg}^{198^{*}}\), where \(\mathrm{Hg}^{198^{*}}\) represents a mercury nucleus in an excited state at energy \(1.063 \mathrm{MeV}\) above the ground state. What can be the maximum kinetic energy of the electron emitted? The atomic masses of \(\mathrm{Au}^{198}\) and \(\mathrm{Hg}^{198}\) are \(197.968 \mathrm{u}\) and \(197.966 \mathrm{u}\), respec- tively. \((1 \mathrm{u}=931.5 \mathrm{MeV})\) (a) \(0.8 \mathrm{MeV}\) (b) \(1.863 \mathrm{MeV}\) (c) \(1.063 \mathrm{MeV}\) (d) \(1.0 \mathrm{MeV}\)

If the amount of radioactive substance is increases three times, the number of disintegration per unit time will be (a) doubled (b) one-third (c) triple (d) uncharged

If a radioactive element is placed in an evacuated container, its rate of disintegration (a) will be increased (b) will be decreased (c) will change very slightly (d) will remain unchanged

Four vessels \(1,2,3\) and 4 contain respectively, 10 g-atom \(\left(t_{1 / 2}=10 \mathrm{~h}\right), 1 \mathrm{~g}\) -atom \(\left(t_{1 / 2}=5 \mathrm{~h}\right), 5\) g-atom \(\left(t_{1 / 2}=2 \mathrm{~h}\right)\) and 2 g-atom \(\left(t_{1 / 2}=1 \mathrm{~h}\right)\) of different radioactive nuclides. In the beginning, the maximum radioactivity would be exhibited by the vessel (a) 4 (b) 3 (c) 2 (d) 1

If \(8 \mathrm{~g}\) of a radioactive isotope has a halflife of \(10 \mathrm{~h}\). The half-life of \(2 \mathrm{~g}\) of the same substance is (a) \(2.5 \mathrm{~h}\) (b) \(5 \mathrm{~h}\) (c) \(10 \mathrm{~h}\) (d) \(40 \mathrm{~h}\)

If \(N_{\mathrm{o}}\) is the initial number of nuclei, number of nuclei remaining undecayed at the end of \(n^{\text {th }}\) half-life is (a) \(2^{n} \cdot N_{\mathrm{o}}\) (b) \(2^{-n} \cdot N_{\mathrm{o}}\) (c) \(n^{2} \cdot N_{\mathrm{o}}\) (d) \(n^{-2} \cdot N_{\mathrm{o}}\)

A radioactive isotope having a half-life of 3 days was received after 12 days. It was found that there were \(3 \mathrm{~g}\) of the isotope in the container. The initial mass of the isotopes when packed was (a) \(12 \mathrm{~g}\) (b) \(24 \mathrm{~g}\) (c) \(36 \mathrm{~g}\) (d) \(48 \mathrm{~g}\)

A freshly prepared radioactive source of half-life \(2 \mathrm{~h}\), emits radiations of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is (a) \(6 \mathrm{~h}\) (b) \(12 \mathrm{~h}\) (c) \(24 \mathrm{~h}\) (d) \(128 \mathrm{~h}\)

Two isotopes 'P' and 'Q' of atomic masses 10 and 20, respectively, are mixed in equal amount, by mass. After 20 day, their mass ratio is found to be \(1: 4 .\) Isotope 'P' has a half-life of 10 days. The half-life of isotope 'Q' is (a) zero (b) 5 day (c) 20 day (d) infinite

A radioactive sample has an initial activity of 28 dpm. Half hour later, the activity is \(14 \mathrm{dpm}\). How many atoms of the radioactive nuclide were there originally? \((\ln 2=0.7)\) (a) 1200 (b) 200 (c) 600 (d) 300

Tritium has a half-life of \(12.26\) years. A \(5.0 \mathrm{ml}\) sample of triturated water has an activity of \(2.4 \times 10^{9} \mathrm{cpm} .\) How many years will it take for the activity to fall to \(3.0 \times 10^{8} \mathrm{cpm} ?\) (a) \(6.13\) (b) \(24.52\) (c) \(36.78\) (d) \(49.04\)

The activity of a certain preparation decreases \(2.5\) times after \(7.0\) days. Find its half-life. (a) \(10.58\) days (b) \(2.65\) days (c) \(5.3\) days (d) \(4.2\) days

An ore of uranium is found to contain \({ }_{92}^{238} \mathrm{U}\) and \({ }_{82}^{206} \mathrm{~Pb}\) in the mass ratio of \(1: 0.1 .\) The half-life period of \({ }_{92}^{238} \mathrm{U}\) is \(4.5 \times 10^{9}\) years. Age of the ore is \((\log 2=0.3, \log\) \(\left.\frac{114.9}{103}=0.048\right)\) (a) \(7.2 \times 10^{8}\) years (b) \(7.2 \times 10^{7}\) years (c) \(7.2 \times 10^{9}\) years (d) \(2.16 \times 10^{9}\) years

In nature a decay chain starts with \(\mathrm{Th}^{232}\) and finally terminates at \(\mathrm{Pb}^{208}\). A thorium ore sample was found to contain \(6.72 \times 10^{-5} \mathrm{ml}\) of \(\mathrm{He}\) (at \(273 \mathrm{~K}\) and \(\left.1 \mathrm{~atm}\right)\) and \(4.64 \times 10^{-7} \mathrm{~g}\) of \(\mathrm{Th}^{232}\). Find the age of the sample assuming that source of He to be only due to decay of \(\mathrm{Th}^{232}\). Also assume complete retention of He within the ore. \(\left(t_{1 / 2}\right.\) of \(\mathrm{Th}^{232}=1.38 \times 10^{10}\) years, \(\log 2=0.3)\) (a) \(2.3 \times 10^{10}\) years (b) \(2.3 \times 10^{9}\) years (c) \(4.6 \times 10^{9}\) years (d) \(9.2 \times 10^{9}\) years

The radioactive series to which \({ }_{88} \mathrm{Ra}^{224}\) belongs is (a) Actinium series (b) Thorium series (c) Uranium series (d) Neptunium series

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) \({ }_{90} \mathrm{Ac}^{227},{ }_{82} \mathrm{~B} \mathrm{i}^{209}\)

Bismuth is the end product of radioactive disintegration series known as (a) \(4 n\) (b) \(4 n+1\) (c) \(4 n+2\) (d) \(4 n+3\)

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) \({ }_{82} \mathrm{~Pb}^{206}\)

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) \(251600 / 8\)

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) \(\lambda / R\)

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) \(67.5 \mathrm{~min}\)

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) \(60 \mathrm{~min}\)

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

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) \({ }_{25} \mathrm{Mn}^{56}\)

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

Which one of the following particles is used to bombard \({ }_{13} \mathrm{Al}^{27}\) to give \({ }_{15} \mathrm{P}^{30}\) and a neutron? (a) \({ }_{1} \mathrm{H}^{2}\) (b) \(\gamma\) (c) \(\alpha\) (d) \(\beta\)

Bombardment of aluminium be \(\alpha\) -particle leads to its artificial disintegration in two way (i) and (ii) as shown. Products \(\mathrm{X}, \mathrm{Y}\) and \(Z\), respectively, are \({ }_{13}^{27} \mathrm{Al} \longrightarrow{ }_{14}^{30} \mathrm{Si}+\mathrm{X}\) \({ }_{13}^{27} \mathrm{Al} \stackrel{\text { (ii) }}{\longrightarrow}{\underline{\phantom{xx}}}_{15}^{30} \mathrm{P}+\mathrm{Y}\) \({ }_{15}^{30} \mathrm{P} \longrightarrow{ }_{14}^{30} \mathrm{Si}+\mathrm{Z}\) (a) proton, neutron, positron (b) neutron, positron, proton (c) proton, positron, neutron (d) positron, proton, neutron