Chapter 27

Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into \(p+\bar{e}+\bar{v}\). If one of the neutrons in Triton decays, it would transform into \(\mathrm{He}^{3}\) nucleus. This does not happen. This is because [NCERT Exemplar] (a) Triton energy is less than that of a \(\mathrm{He}^{3}\) nucleus. (b) The electron created in the beta decay process cannot remain in the nucleus. (c) both the neutrons in trition have to decay simultaneously resulting in a nucleus with 3 protons, which is not a \(\mathrm{He}^{3}\) nucleus. (d) because free neutrons decay due to external perturbations which is absent in a triton nucleus.

Question No. 69 to 76 are Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choice from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion If the half-life of a radioactive substance is 40 days then \(25 \%\) substance decays in 20 days. Reason \(\quad N=N_{0}\left(\frac{1}{2}\right)^{n}\) where \(n=\frac{\text { time elapsed }}{\text { half-life period }}\)

The half-life of radioactive Radon is \(3.8\) days. The time at the end of which ( \(1 / 20\) )th of the Radon sample will remain undecayed is (given \(\log _{10} e=0.4343\) ) (a) \(13.8\) days (b) \(16.5\) days (c) 33 days (d) 76 days

A radioactive isotope has a half-Ifie of \(T\) years. How long will it take the activity to reduce to (a) \(4.5 \mathrm{~T}\) and \(7.5 \mathrm{~T}\) (b) \(9.5 \mathrm{~T}\) and \(5 \mathrm{~T}\) (c) \(5 \mathrm{~T}\) and \(9.5 \mathrm{~T}\) (d) \(5 \mathrm{~T}\) and \(6.65 \mathrm{~T}\)

Assertion Balmer series lies in the visible region of electromagnetic spectrum. Reason \(\frac{1}{\lambda}=R\left(\frac{1}{2^{2}}-\frac{1}{n^{2}}\right)\), where \(n=3,4,5 \ldots\)

Half-life of radium is \(1600 \mathrm{yr}\). Its average life is (a) \(3200 \mathrm{yr}\) (b) \(4800 \mathrm{yr}\) (c) \(2308 \mathrm{yT}\) (d) \(4217 \mathrm{yr}\)

Plutonium decays with half-life of 24000 yr. If plutonium is stored for \(7200 \mathrm{yr}\), the fraction of it that remains is (a) \(1 / 8\) (b) \(1 / 3\) (c) \(1 / 4\) (d) \(1 / 2\)

Assertion All nuclei are not of same size. Reason Size depends on atomic mass.

The penetrating powers of \(\alpha, \beta\) and \(\gamma\) radiations, in decreasing order are (a) \(v, \alpha, \beta\) (b) \(\gamma, \beta, \alpha\) (c) \(\alpha, \beta, \gamma\) (d) \(\beta, \gamma, \alpha\)

Assertion \(1 \mathrm{amu}\) is equivalent to \(931 \mathrm{MeV}\). Reason Energy equivalent \((E)\) or mass \((m)\) is \(E=m c^{2} .\)

Assertion \({ }_{38} \mathrm{Sr}^{90}\) from the radioactive fall out from a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of the production of red blood cells. Reason The energy \(\beta\)-particle emitted in the decay of \({ }^{90} \mathrm{Sr}\) damage to bone marrow.

After absorbing a slowly moving neutron of mass \(n_{N}\) (momentum \(\sim 0\) ) a nucleus of mass \(M\) breaks into two nuclei of masses \(m_{1}\) and \(5 m_{1}\left(6 m_{1}=M+m_{N}\right)\), respectively. If the de-Broglie wavelength of the nucleus with mass \(m_{1}\) is \(\lambda\), then de-Broglie wavelength of the other nucleus will be (a) \(25 \lambda\) (b) \(5 \lambda\) (c) \(\frac{\lambda}{5}\) (d) \(\lambda\)

A radioactive nucleus can decay simultaneously by two different processes which have decay constant \(\lambda_{1}\) and \(\lambda_{2} .\) The effective decay constant of the nuclide is \(\lambda\), where (a) \(\lambda=\lambda_{1}+\lambda_{2}\) (b) \(\lambda=2\left(\lambda_{1}+\lambda\right)\) (c) \(\frac{1}{\lambda}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}\) (d) \(\lambda=\sqrt{\lambda_{1} \lambda_{2}}\)

Directions This question contain statement I and statement II. Of the four choices given after the statements, choice the one that best describes the two statements: (a) Statement 1 is true, Statement 11 is true; Statement 11 is the correct explanation of Statement 1 (b) Statement 1 is true, Statement 11 is true; Statement 11 is not the correct explanation of Statement 1 (c) Statement 1 is false, Statement 11 is true (d) Statement 1 is true, Statement \(\mathrm{ll}\) is false Statement I When ultraviolet light is incident on a photocell, its stopping potential is \(V_{0}\) and the maximum kinetic energy of the photoelectrons is \(K_{\max } .\) When the ultraviolet light is replaced by X-rays, both \(V_{0}\) and \(K_{\max }\) increase. Statement II Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

The half-life period of radium is \(1600 \mathrm{yr}\). The fraction of a sample of radium that would remain after \(6400 \mathrm{yr}\) is (a) \(\frac{1}{4}\) (b) \(\frac{1}{2}\) (c) \(\frac{1}{8}\) (d) \(\frac{1}{16}\)

If a source of power \(4 \mathrm{~kW}\) produces \(10^{20}\) photons/sec the radiation belongs to a part of the spectrum called (a) \(\gamma\)-rays (b) X-rays (c) UV-rays (d) microwaves

Two radioactive sources \(A\) and \(B\) of half lives \(1 \mathrm{~h}\) and 2h respectively initially contain the same number of radioactive atoms. At the end of two hours, their rates of disintegration are in the ratio of (a) \(1: 4\) (b) \(1: 3\) (c) \(1: 2\) (d) \(1: 1\)

In a cathode ray oscillograph, the focusing of beam on the screen is achieved by (a) convex lenses (b) magnetic field (c) electric potential (d) All of these

The normal activity of living carbon containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive \({ }_{6}^{14} \mathrm{C}\) present with the stable carbon isotope \({ }_{6}^{12} \mathrm{C}\). when the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life \((5730 \mathrm{yr})\) of \({ }_{6}^{14} \mathrm{C}\) and the measured activity, the age of the specimen can be approximately estimated. This is the principle of \({ }_{6}^{14} \mathrm{C}\) dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilization. (a) \(5224 \mathrm{yr}\) (b) \(4224 \mathrm{yr}\) (c) \(8264 \mathrm{yr}\) (d) \(6268 \mathrm{yr}\)

A wrong argument of the particle nature of cathode rays is that they (a) produce fluorescence (b) travel through vacuum (c) get deflected by electric and magnetic fields (d) cast shadow

Half-life of radioactive substance is 140 days. Initially, is \(16 \mathrm{~g}\). Calculate the time for this substance when it reduces to \(1 \mathrm{~g}\) (a) 140 days (b) 280 days (c) 420 days (d) 560 days

An X-ray tube produces a continuous spectrum of radiation with its shortest wavelength of \(45 \times 10^{-2} \AA\). The maximum energy of a photon in the radiation in \(\mathrm{eV}\) is \(\left(h=6.62 \times 10^{-34} \mathrm{~J}-\mathrm{s}, c=3 \times 10^{8} \mathrm{~ms}^{-1}\right)\) (a) 27,500 (b) 22,500 (c) 17,500 (d) 12,500

1 Fusion process, line combining two deutrons to form a He nucleus are impossible at ordinary temperatures and pressure. This reasons for this can be traced to the fact [NCERT Exemplar] (a) nuclear forces have short range (b) nuclei are positively charge (c) the original nuclei must be completely ionized before fussion can take place (d) the original nuclei must first break up before combining with each other.

Millikan's oil drop experiment establish that (a) electric charge depends on velocity (b) electron has wave nature (c) electric charge is quantised (d) electron has particle nature (e) electron has wave nature

Which one of the following statements is wrong in the context of X-rays generated from a X-rays tube? (a) Wavelength of characteristic X-rays decreases when the atomic number of the target increases (b) Cut-off wavelength of the continuous \(X\)-rays depends on the atomic number of the target (c) Intentsity of the characteristic \(X\)-rays depends on the electrical power given to the \(X\)-rays tube (d) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the \(X\)-ray tube

A moderator is used in nuclear reactors in order to (a) slow down the speed of the neutrons (b) accelerate the neutrons (c) increase the number of neutrons (d) decrease the number of neutrons

If \(g_{E}\) and \(g_{m}\) are the accelerations due to gravity on the surfaces of the earth and moon respectively and if Millikan's oil drop experiment and the performed on the two surfaces one will be find the ratio \(=\frac{\text { electronic charge on the moon }}{\text { electronic charge on the earth }}\) to be (a) 1 (b) 0 (c) \(\frac{g_{E}}{g_{m}}\) (d) \(\frac{g_{m}}{g_{E}}\)

During a nuclear fusion reaction (a) A heavy nucleus breaks into two fragments by itself (b) A light nucleus bombarded by thermal neutrons break up (c) A heavy nucleus bombarded by thermal neutrons break up (d) Two light nuclei combine to give a heavier nucleus and possible other products

A metallic surface is irradiated by a monochromatic light of frequency \(v_{1}\) and stopping potential is found to be \(V_{1}\). If the light of frequency \(v_{2}\) irradiates the surface, the stopping potential will be (a) \(V_{1}+\frac{h}{e}\left(v_{1}+v_{2}\right)\) (b) \(V_{1}+\frac{h}{e}\left(v_{2}-v_{1}\right)\) (c) \(v_{1}+\frac{e}{h}\left(v_{2}-v_{1}\right)\) (d) \(V_{1}+\frac{h}{e}\left(v_{1}-v_{2}\right)\) (e) \(V_{1}-\frac{\mathrm{e}}{h}\left(v_{2}-v_{1}\right)\)

The nucleus \({ }_{6} \mathrm{C}^{2}\) absorbs an energetic neutron and emits a \(\beta\)-particle. The resulting nucleus is (a) \({ }_{7} \mathrm{~N}^{14}\) (b) \({ }_{5} \mathrm{~B}^{13}\) (c) \({ }_{7} \mathrm{~N}^{13}\) (d) \({ }_{6} \mathrm{C}^{13}\)

The longest wavelength that can be analysed by a sodium chloride crystal of spacing \(d=2.82 \AA\) in the second order is (a) \(2.82 \AA\) (b) \(5.64 \overline{\mathrm{A}}\) (c) \(8.46 \AA\) (d) \(11.28 \AA\)

In the uranium radioactive series, the initial nucleus is \({ }_{92} \mathrm{U}^{238}\) and that the final nucleus is \({ }_{82} \mathrm{~Pb}^{206}\). When uranium nucleus decays to lead, the number of \(\alpha\)-particle and \(\beta\)-particles emitted are (a) \(8 \alpha, 6 \beta\) (b) \(6 \alpha, 7 \beta\) (c) \(6 \alpha, 8 \beta\) (d) \(4 \alpha, 3 \beta\)

Complete the equation for the following fission process \({ }_{92} \mathrm{U}^{235}+{ }_{0} n^{1} \longrightarrow \ldots 38 \mathrm{Kr}^{90}+\ldots\) (a) \(_{50} X e^{143}+3_{0} n^{1}\) (b) \(_{54} X e^{145}\) (c) \(_{57} X e^{142}\) (d) \({ }_{54} \mathrm{Xe}^{142}+{ }_{0} n^{1}\)

In Millikan's oil drop experiment on oil drop of mass \(16 \times 10^{-6} \mathrm{~kg}\) is balanced by a electric field of \(10^{6} \mathrm{Vm}^{-1}\). The charge in coulomb on the drop will be \(\left(g=10 \mathrm{~ms}^{-2}\right)\) (a) \(16 \times 10^{-13} \mathrm{C}\) (b) \(16 \times 10^{-11} \mathrm{C}\) (c) \(6.2 \times 10^{-11} \mathrm{C}\) (d) \(16 \times 10^{-9} \mathrm{C}\)

A source contains two phosphorous radio nuclides \({ }_{15}^{32} \mathrm{P}\left(T_{1 / 2}=14.3\right.\) days) and \({ }_{15}^{33} \mathrm{P}\left(T_{1 / 2}=25.3\right.\) days). Initially, \(10 \%\) of the decay come from \({ }_{15}^{33} \mathrm{P}\). How long one must wait until \(90 \%\) do so? (a) 250 days (b) 295 days (c) 305 days (d) 208 days

Assertion (A) If an accelerating potential in a X-ray tube is increased, the wavelength of the characteristic X-ray do not change. Reason (R) When an electric beam strikes the target in an X-ray tube, part of KE is converted into X-ray equation. (a) A is true, \(\mathrm{R}\) is true, \(\mathrm{R}\) is correct explanation of \(\mathrm{A}\) (b) A is true, \(R\) is true, but \(R\) is not correct explanation of \(A\) (c) \(\mathrm{A}\) is true, \(\mathrm{R}\) is false (d) \(\mathrm{A}\) is false, \(\mathrm{R}\) is true

If the mass of a radioactive sample is doubled, the activity of the sample and the disintegration constant of the sample are respectively. (a) Increases, remains the same (b) Decreases, increases (c) Decreases, remains same (d) Increases, decreases

Monochromatic light incident on a metal surface emits electrons with kinetic energies from zero to \(2.6 \mathrm{eV}\). What is the least energy of the incident photon, if the tightly bound electron needs \(4.2 \mathrm{eV}\) to remove? (a) \(1.6 \mathrm{~V}\) (b) From \(1.6 \mathrm{eV}\) to \(6.8 \mathrm{eV}\) (c) \(6.8 \mathrm{eV}\) (d) More than \(6.8 \mathrm{eV}\)

Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is \((14)^{1 / 3}\). The atomic number of nucleus will be (a) 25 (b) 26 (c) 56 (d) 30

A photocell is illuminated by a small bright source placed \(1 \mathrm{~m}\) away. When the same source of light is placed \(\frac{1}{2} \mathrm{~m}\) away, the number of electrons emitted by photo cathode would (a) increase by a factor of 2 (b) decrease by a factor of 2 (c) increase by a factor of 4 (d) decrease by a factor of 4

This question has Statement I and Statement II. Of the four choices given the statements, choose the one that describes the two statements. Statement I Davisson-Gerner experiment established the wave nature of electrons. Statement II If electrons have wave nature, they can interfere and show diffraction. (a) Statement 1 is false, Statement 11 is true. (b) Statement 1 is true, Statement \(\|\) is false. (c) Statement 1 is true, Statement 11 is true, Statement \(\|\) is the correct explanation for statement 1 (d) Statement 1 is true, statement 11 is true, statement \(\mathrm{ll}\) is not the correct explanation of statement 1 .

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4 . Then, the number of spectral lines in the emission spectra will be (a) 2 (b) 3 (c) 5 (d) 6

The half-life of a radioactive substance is \(20 \mathrm{~min}\). The approximate time interval \(\left(t_{2}-t_{1}\right)\) between the time \(t_{2}\) when \(\frac{2}{3}\) of it has decayed and time \(t_{1}\) when \(\frac{1}{3}\) of it had decayed is (a) \(14 \mathrm{~min}\) (b) \(20 \mathrm{~min}\) (c) \(28 \mathrm{~min}\) (d) \(7 \mathrm{~min}\)

After absorbing a slowly moving neutron of mass \(M_{N}\) comonecular a nucleus of mass \(M\) breaks into two nuclei of masses \(m_{1}\) and \(5 m_{1}\left(6 m_{1}=M+m_{N}\right)\), respectively. If the de-Broglie wavelength of the nucleus with mass \(m\), is \(\lambda\), then de-Broglie wavelength of the other nucleus will be (a) \(25 \lambda\) (b) \(5 \lambda\) (c) \(\frac{\lambda}{5}\) (d) \(\lambda\)

A diatomic molecule has moment of inertia \(I\). By Bohr's quantization condition its rotational energy in the \(n\)th level \((n=0\) is not allowed) is (a) \(\frac{1}{n^{2}}\left(\frac{h^{2}}{8 \pi^{2} l}\right)\) (b) \(\frac{1}{n}\left(\frac{h^{2}}{8 \pi^{2} l}\right)\) (c) \(n\left(\frac{h^{2}}{8 \pi^{2} I}\right)\) (d) \(n^{2}\left(\frac{h^{2}}{8 \pi^{2} 1}\right)\)

It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to \(\frac{4}{\pi} \times 10^{11} \mathrm{~Hz}\). Then the moment of inertia of CO molecule about is centre of mass is close to (take \(h=2 \pi \times 10^{-34} \mathrm{~J}\)-s) (a) \(2.76 \times 10^{-46} \mathrm{kgm}^{2}\) (b) \(1.87 \times 10^{-46} \mathrm{kgm}^{2}\) (c) \(4.67 \times 10^{-47} \mathrm{kgm}^{2}\) (d) \(1.17 \times 10^{-47} \mathrm{kgm}^{2}\)

Statement I A nucleus having energy \(E_{1}\) decays be \(\beta^{-}\) emission to daughter nucleus having energy \(E_{2}\), but the \(\beta_{2}\) rays are emitted with a contribution energy spectrum having end point energy \(E_{1}-E_{2}\). Statement II To conserve energy and momentum in \beta-decay at least three particles must take part in the transformation. (a) Statement \(\mathrm{l}\) is false, Statement II is true. (b) Statement 1 is true, Statement 11 is false. (c) Statement 1 is true, Statement II is true, Statement 11 is the correct explanation of Statement 1 . (d) Statement 1 is true, Statement 11 is true, Statement \(\|\) is not the correct explanation of Statement 1 .