Chapter 27

Hydrogen atoms are excited from ground state of the principal quantum number \(4 .\) Then, the number of spectral lines observed will be (a) 3 (b) 6 (c) 5 (d) 2

The half-life of \({ }^{215}\) At is \(100 \mu \mathrm{s}\). The time taken for the cadioactivity of a sample of \({ }^{215}\) At to decay to \(\frac{1}{16}\) th of its initial value is (a) \(400 \mu \mathrm{s}\) (b) \(6.3 \mu \mathrm{s}\) (c) \(40 \mu \mathrm{s}\) (d) \(300 \mu \mathrm{s}\)

What is the de-Broglie wavelength of a nitrogen molecule in air at \(300 \mathrm{~K}\) ? Assume that the molecule is moving with the root-mean-square speed of molecules at this temperature. (Atomic mass of nitrogen \(=14.0076 \mathrm{u}\) ) \(\quad\) [NCERT] (a) \(0.01 \mathrm{~nm}\) (b) \(0.09 \mathrm{~nm}\) (c) \(0.03 \mathrm{~nm}\) (d) \(0.2 \mathrm{~nm}\)

A nucleus of \({ }_{84} \mathrm{Po}^{210}\) originally at rest emits an \(\alpha\)-particle with speed \(v\). What will be recoil speed of the daughter nucleus? (a) \(4 v / 206\) (b) \(4 v / 214\) (c) \(v / 206\) (d) \(v / 214\)

When a hydrogen atom is bombared, the atom is excited to then \(n=4\) state. The energy released, when the atom goes from \(n=4\) state to the ground state is (a) \(1.75 \mathrm{eV}\) (b) \(12.75 \mathrm{eV}\) (c) \(5 \mathrm{eV}\) (d) \(8 \mathrm{eV}\)

The radioactivity isotope \(X\) with a half-life of \(10^{9}\) year decays to \(Y\) which is stable. A sample of rocks were found to contain both the elements \(X\) and \(Y\) in the ratio \(1: 7\). What is the age of the rocks? (a) \(2 \times 10^{9} \mathrm{yr}\) (b) \(3 \times 10^{9} \mathrm{yr}\) (c) \(6 \times 10^{9} \mathrm{yr}\) (d) \(7 \times 1^{9} \mathrm{yr}\)

An electron jumps from the 4 th orbit to 2 nd orbit of hydrogen atom. Given the Rydberg's constant \(R=10^{5} \mathrm{~cm}^{-1}\), the frequency in hertz of the emitted radiation will be (a) \(\frac{3}{16} \times 10^{5}\) (b) \(\frac{3}{16} \times 10^{15}\) (c) \(\frac{9}{16} \times 10^{15}\) (d) \(\frac{3}{4} \times 10^{15}\)

The ratio of molecular mass of two radioactive substances is \(3 / 2\) and the ratio of their decay constants is \(4 / 3\). Then, the ratio of their initial activity per mole will be (a) 2 (b) \(4 / 3\) (c) \(8 / 9\) (d) \(9 / 8\)

The energy of an electron in \(n\)th orbit of the hydrogen atom is given by \(E_{n}=\frac{-13.6}{n^{2}} \mathrm{eV}\). The energy required to raise an electron from, the first orbit to the second orbit will be (a) \(10.2 \mathrm{eV}\) (b) \(12.1 \mathrm{eV}\) (c) \(13.6 \mathrm{eV}\) (d) \(3.4 \mathrm{eV}\)

For the ground state the electron in the H-atom has an angular momentum \(=h\), according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true, [NCERT Exemplar] (a) because Bohr model gives incorrect values of angular momentum. (b) because only one of these would have a minimum energy. (c) angular momentum must be in the direction of spin of electron. (d) because electrons go around only in horizontal orbits.

A radioactive substance of half-life 6 min is placed near a Geiger counter which is found to register 1024 particles per minute. How many particles per minute will it register after 42 min? (a) 4 per min (b) 8 per min (c) 5 per min (d) 7 per \(\min\)

For light of wavelength \(5000 \AA\), photon energy is nearly \(2.5 \mathrm{eV}\). For \(X\)-rays of wavelength \(1 \AA\), the photon energy will be close to [a) \([2.5 \div 5000] \mathrm{eV}\) (b) \(\left[2.5 \div(5000)^{2}\right] \mathrm{eV}\) (c) \([2.5 \times 5000] \mathrm{eV}\) (d) \(\left[2.5 \times(5000)^{2}\right] \mathrm{eV}\)

The half-life for the ?-decay of uranium \({ }_{92} \mathrm{U}^{238}\) is \(4.47 \times 10^{9} \mathrm{yr}\). If a rock contains sixty percent of its original \({ }_{92} \mathrm{U}^{238}\) atoms, its age is \([\log 6=0.778 ; \log 2=0.3]\) (a) \(3.3 \times 10^{9} \mathrm{yr}\) (b) \(6.6 \times 10^{9} \mathrm{yr}\) (c) \(1.2 \times 10^{8} \mathrm{yr}\) (d) \(5.4 \times 10^{7} \mathrm{yr}\)

Consider an electron in the \(n\)th orbit of a hydrogen atom in the Bohr model. The circumference of the 5 orbit can be expressed in terms of the de-Broglie wavelength of that electron as (a) \((0.529) n \lambda\) (b) \(\sqrt{n} \lambda\) (c) \((13.6) \lambda\) (d) \(n \lambda\)

The electron in a hydrogen atom makes a transition from \(n=n_{1}\) to \(n=n_{2}\) state. The time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are (a) \(n_{1}=6, n_{2}=2\) (b) \(n_{1}=2, n_{2}=1\) (c) \(n_{1}=8, n_{2}=2\) (d) \(n_{1}=4, n_{2}=2\)

\(\mathrm{O}_{2}\) molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms. (a) is not important because nuclear forces are short-ranged (b) is as important as electrostatic force for binding the two atoms. (c) cancels the repulsive electrostatic force between the nuclei (d) is not important because oxygen nucleus have equal number of neutrons and protons.

Which energy state of the triply ionized beryllium has the same electron orbital radius as that of ground state of hydrogen? Given \(\mathrm{Z}\) for \(\mathrm{Be}=4\) (a) \(n=4\) (b) \(n=3\) (c) \(n=2\) (d) \(n=1\)

The electron in a hydrogen atom makes a transition \(n_{1} \rightarrow n_{2}\) where \(n_{1}\) and \(n_{2}\) are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of electron in the initial state is 8 times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are (a) \(n_{1}=6, n_{2}=3\) (b) \(n_{1}=8 n_{2}=2\) (c) \(n_{1}=n_{2}=1\) (d) \(n_{1}=8, n_{2}=1\)

The ratio of the energies of the hydrogen atom in its first to second excited states is (a) \(9 / 4\) (b) \(4 / 1\) (c) \(8 / 1\) (d) \(1 / 8\)

There are two radioactive substances \(A\) and \(B\). Decay constant of \(B\) is two times that of \(A\). Initially, both have equal number of nuclei. After \(n\) half-lives of \(A\), rate of disintegration of both are equal. The value of \(n\) is (a) 4 (b) 2 (c) 1 (d) 5

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the \(n=4\) level. Determine the wavelength and frequency of photon. (a) \(9.7 \times 10^{-8} \mathrm{~m}\) and \(3.1 \times 10^{15} \mathrm{~Hz}\) (b) \(7.6 \times 10^{-9} \mathrm{~m}\) and \(2.6 \times 10^{14} \mathrm{~Hz}\) (c) \(2.9 \times 10^{-10} \mathrm{~m}\) and \(4.9 \times 10^{12} \mathrm{~Hz}\) (d) \(8.6 \times 10^{-9} \mathrm{~m}\) and \(3.1 \times 10^{14} \mathrm{~Hz}\)

The binding energy of an electron in the ground state of He is equal to \(24.6 \mathrm{eV}\). The energy required to remove both the electrons is (a) \(49.2 \mathrm{eV}\) (b) \(24.6 \mathrm{eV}\) (c) \(38.2 \mathrm{eV}\) (d) \(79.0 \mathrm{eV}\)

An \(\alpha\)-particle of energy \(5 \mathrm{MeV}\) is scattered through \(180^{\circ}\) by a fixed uranium nucleus. The distance of closest approach is of the order of (a) \(1 \mathrm{~A}\) (b) \(10^{-10} \mathrm{~cm}\) (c) \(10^{-12} \mathrm{~cm}\) (d) \(10^{-15} \mathrm{~cm}\)

An X-ray tube is operating at \(50 \mathrm{kV}\) and \(20 \mathrm{~mA}\). The target material of the tube has a mass of \(1 \mathrm{mg}\) and specific heat \(495 \mathrm{~J} \mathrm{~kg}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1} .\) One per cent of the supplied electric power is converted into \(X\)-rays and the entire remaining energy goes into heating the target. Then (a) a suitable target material must have a high the melting temperature (b) a suitable target material must have low thermal conductivity (c) the average rate of use of temperature of target would be \(2^{\circ} \mathrm{C} / \mathrm{s}\) (d) the minimum wavelength of the \(X\)-rays emitted is about \(0.25 \times 10^{-10} \mathrm{~m}\)

Ionization potential of hydrogen atom is \(13.6 \mathrm{eV}\). Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy \(12.1 \mathrm{eV}\). The spectral lines emitted by hydrogen atom according to Bohr's theory will be (a) one (b) two (c) three (d) four

When a monochromatic point source of light is at a distance of \(0.2 \mathrm{~m}\) from a photo electric cell, the cut off voltage and the saturation currents are respectively \(0.6 \mathrm{v}\) and \(18.0 \mathrm{~mA}\). If, the same source is placed \(0.6 \mathrm{~m}\) away from the photoelectric cell, then (a) the stopping potential will be \(0.2 \mathrm{~V}\) (b) the stopping potential will be \(0.6 \mathrm{~V}\) (c) the saturation current will be \(0.6 \mathrm{~mA}\) (d) the saturation current will be \(0.2 \mathrm{~mA}\)

The first line of Balmer series has wavelength \(6563 \AA\). What will be the wavelength of the first member of Lyman series? (a) \(1215.4 \mathrm{~A}\) (b) \(2500 \mathrm{~A}\) (c) \(7500 \mathrm{~A}\) (d) \(600 \mathrm{~A}\)

Two H atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic energy is reduced is (a) \(10.20 \mathrm{eV}\) (b) \(20.40 \mathrm{eV}\) (c) \(13.6 \mathrm{eV}\) (d) \(27.2 \mathrm{eV}\)

Electric conduction takes place in a discharge tube due to movement of (a) positive ions (b) negative ions (c) electrons (d) photons

The wave number of the energy emitted when electron comes from fourth orbit to second orbit in hydrogen is \(20,397 \mathrm{~cm}^{-1}\). The wave number of the energy for the same transition in \(\mathrm{He}^{+}\)is (a) \(5,099 \mathrm{~cm}^{-1}\) (b) \(20,497 \mathrm{~cm}^{-1}\) (c) \(14400 \mathrm{~A}\) (d) \(81,588 \mathrm{~cm}^{-1}\)

An electron in hydrogen atom first jumps from second excited state to first excited state and then from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be \(a, b\) and \(c\) respectively. Then (a) \(a=\frac{9}{4}\) (b) \(b=\frac{5}{27}\) (c) \(c=\frac{5}{27}\) (d) \(c=\frac{1}{a}\)

In the Bohr model of the hydrogen atom, let \(R, V\) and \(E\) represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantities is proportional to quantum number \(n ?\) (a) \(\frac{R}{E}\) (b) \(\frac{E}{V}\) (c) \(R \bar{E}\) (d) \(V \underline{R}\)

An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state, \(\quad\) [NCERT Exemplar] (a) the electron would not move in circular orbits. (b) the energy would be \((2)^{4}\) times that of a h-atom. (c) the electrons, orbit would go around the protons. (d) the molecule will soon decay in a proton and a H-atom.

Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom. [NCERT Exemplar] (a) because of energy conservation (b) without simultaneously releasing energy in the form of radiation (c) because of momentum conservation (d) because of angular momentum conservation

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year [NCERT Exemplar] (a) all the containers will have 5000 atoms of the materials. (b) all the containers will contain the same number of atoms of the material but that number will only be approximately \(5000 .\) (c) the containers will in general have different numbers of the the atoms of the material but their average will be close to 5000 . (d) None of the containers can have more than 5000 atoms.

The energy, the magnitude of linear momentum and orbital radius of an electron in a hydrogen atom corresponding to the quantum number \(n\) are \(E, P\) and \(r\) respectively. Then according to Bohr's theory of hydrogen atom, (a) \(P r\) is proportional to \(n\) (b) \(P / E\) is proportional to \(n\) (c) \(E r\) is constant for all orbits (d) \(E P r\) is proportional to \(1 / n\)

A If Avogadro number is \(6 \times 10^{23}\), then number of protons, neutrons and electrons is \(14 \mathrm{~g}\) of \({ }_{6} \mathrm{C}^{14}\) are respectively (a) \(36 \times 10^{23}, 48 \times 10^{23}, 36 \times 10^{23}\) (b) \(36 \times 10^{23}, 36 \times 10^{23}, 36 \times 10^{23}\) (c) \(48 \times 10^{23}, 36 \times 10^{23}, 48 \times 10^{23}\) (d) \(48 \times 10^{23}, 48 \times 10^{23}, 36 \times 10^{23}\) \(\mathrm{F}\)

Let \(E_{n}=\frac{-1}{8 \varepsilon_{0}^{2} n^{2} h^{2}}\) be the energy of the \(n\)th level of H-atom. If all the H-atoms are in the ground state and radiation of frequency \(\left(E_{2}-E_{1}\right) / \mathrm{h}\) falls on it. [NCERT Exemplar] (a) it will not be absorbed at all (b) some of atoms will move to the first excited state (c) all atoms will be excited to the \(n=2\) state. (d) no atoms will make a transition to the \(n=3\) state

The binding energies per nucleon of \(\mathrm{Li}^{7}\) and \(\mathrm{He}^{4}\) are \(5.6 \mathrm{MeV}\) and \(7.06 \mathrm{MeV}\) respectively, then the energy of the reaction \(\mathrm{Li}^{7}+p=2\left[{ }_{2} \mathrm{He}^{4}\right]\) will be (a) \(17.28 \mathrm{MeV}\) (b) \(39.2 \mathrm{MeV}\) (c) \(28.24 \mathrm{MeV}\) (d) \(1.46 \mathrm{MeV}\)

\(M_{x}\) and \(M_{y}\) denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The \(Q\)-value of a \(\beta^{-}\)decay is \(Q_{1}\) and that for a \(\beta^{+}\) decay is \(Q_{2}\). If \(m_{e}\) denotes the mass of an electron, then which of the following statements is correct? [NCERT Exemplar] (a) \(Q_{1}=\left(M_{x}-M_{y}\right) c^{2}\) and \(Q_{2}=\left(M_{x}-M_{y}-2 m_{e}\right) c^{2}\) (b) \(Q_{1}=\left(M_{x}-M_{y}\right) c^{2}\) and \(Q_{2}=\left(M_{x}-M_{y}\right) c^{2}\) (c) \(Q_{1}=\left(M_{x}-M_{y}-2 m_{e}\right) c^{2}\) and \(Q_{2}=\left(M_{x}-M_{y}+2 m_{e}\right) c^{2}\) (d) \(Q_{1}=\left(M_{x}-M_{y}+2 m_{e}\right) c^{2}\) and \(Q_{2}=\left(M_{x}-M_{y}+2 m_{e}\right) c^{2}\)

Samples of two radioactive nuclides \(A\) and \(B\) are taken. \(\lambda_{A}\) and \(\lambda_{B}\) are the disintegration constants of \(A\) and \(B\) respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time ? [NCERT Exemplar] (a) Initial rate of decay of \(A\) is twice the initial rate of decay of \(B\) and \(\lambda_{A}=\lambda_{B}\) (b) Initial rate of decay of \(A\) is twice the initial rate of decay of \(B\) and \(\lambda_{A}>\lambda_{B}\) (c) Initial rate of decay of \(B\) is twice the initial rate of decay of \(A\) and \(\lambda_{A}>\lambda_{B}\). (d) Initial rate of decay of \(B\) is same as the rate of decay of \(A\) at \(t=2 h\) and \(\lambda_{B}<\lambda_{A}\).

The binding energy of two nuclei \(p^{n}\) and \(Q^{2 n}\) are \(x\) joule and \(y\) joule respectively. If \(2 x>y\), then the energy released in the reaction \(p^{n}+p^{n}=Q^{2 n}\) will be (a) \(2 x+y\) (b) \(2 x-y\) (c) \(x y\) (d) \(x+y\)

Energy released in the fission of a single nucleus is \(200 \mathrm{MeV}\). The fission rate of a \({ }_{92}^{235} \mathrm{U}\) filled reactor operating at a power level of \(5 \mathrm{~W}\) is (a) \(1.56 \times 10^{-10} \mathrm{~s}^{-1}\) (b) \(1.56 \times 10^{11} \mathrm{~s}^{-1}\) (c) \(1.56 \times 10^{-16} \mathrm{~s}^{-1}\) (d) \(1.56 \times 10^{-17} \mathrm{~s}^{-1}\)

Total energy of electron in first stationary orbit of hydrogen atom is \(-13.6 \mathrm{eV}\). The energy in second stationary orbit would be (a) \(13.6 \mathrm{eV}\) (b) \(8.6 \mathrm{eV}\) (c) \(-13.6 \mathrm{eV}\) (d) \(-3.4 \mathrm{eV}\)

Two nucleons are at a separation of \(1 \mathrm{fm}\). The net force between them is \(F_{1}\), if both neutrons, \(F_{2}\) if both are protons and \(F_{3}\) if one is a proton and the other is a neutron. (a) \(F_{1}>F_{2}>F_{3}\) (b) \(F_{2}>F_{1}>F_{3}\) (c) \(F_{1}=F_{3}>F_{1}\) (d) \(F_{1}=F_{2}>F_{3}\)

The energy released when an electron jumps from second stationary orbit to the first stationary orbit in hydrogen atom is (a) \(10.2 \mathrm{eV}\) (b) \(-10.2 \mathrm{eV}\) (c) \(3.4 \mathrm{eV}\) (d) \(13.6 \mathrm{eV}\)

The energy equivalent of one atomic mass unit is (a) \(1.6 \times 10^{-19} \mathrm{~J}\) (b) \(6.02 \times 10^{-23} \mathrm{~J}\) (c) \(931 \mathrm{~J}\) (d) \(931 \mathrm{MeV}\)

Match the following Column I with Column II Column I \(\quad\) Column II Column 1. I. Nuclear fusion II. Mass defect III. Nuclear reaction IV. Nuclear reactor Column II A. \(E=m c^{2}\) B. Moderator C. Stellar energy D. Binding energy Codes (a) I-C, II-D, III-A, IV-B (b) I-A, II-B, III-C, IV-D (c) II-D, I-A, III-C, IV-A (d) I-C, II-B, III-A, IV-D

\({ }_{92} \mathrm{U}^{235}\) and \({ }_{92} \mathrm{U}^{238}\) differ as (a) \({ }_{92} \mathrm{U}^{235}\) has 2 protons less (b) \({ }_{92} \mathrm{U}^{238}\) has 3 protons more (c) \({ }_{92} \mathrm{U}^{238}\) has 3 neutrons more (d) None of the above

Match the following Column I with Column II Column 1 I. Thomson atomic model II. Rutherford Atom III. Bohr atom model IV. Ionisation potential Column II A. Fixed for an atom B. Stationary orbits model C. Charge and mass are distributed uniformly in a sphere D. Nucleus Codes (a) 1-A, 11-B, III-C, IV-D (b) \(1-\mathrm{D}, 11-\mathrm{B}, \mathrm{lll}-\mathrm{A}, \mathrm{IV}-\mathrm{C}\) (c) 1-C, 11-D, III-B, IV-A (d) 1-A, 11-C, 111-D, IV-B