Chapter 27

Doubly ionised helium atom and hydrogen ions are accelerated, from rest, through the same potential difference. The ratio of final velocities of helium and hydrogen is (a) \(1: \sqrt{2}\) (b) \(\sqrt{2}: 1\) (c) \(1: 2\) (d) \(2: 1\)

In Thomson's mass spectrographs, when an electric field of \(2 \times 10^{4} \mathrm{Vm}^{-1}\) is applied, then the deflection produced on the screen is \(20 \mathrm{~mm}\). If the length of the plates is \(5 \mathrm{~cm}\) and the distance of the screen from plates is \(21 \mathrm{~cm}\) and the velocity of positive ions is \(10^{6} \mathrm{~ms}^{-1}\), then their specific charge will be (a) \(10^{7} \mathrm{Ckg}^{-1}\) (b) \(2.59 \times 10^{7} \mathrm{Ckg}^{-1}\) (c) \(5.9 \times 10^{7} \mathrm{Ckg}^{-1}\) (d) \(9.52 \times 10^{7} \mathrm{Ckg}^{-1}\)

Mixed \(\mathrm{He}^{+}\)and \(\mathrm{O}^{2+}\) ions (mass of \(\mathrm{He}^{+}=4\) amu and that of \(\mathrm{O}^{2+}=16 \mathrm{amu}\) ) beam passes a region of constant perpendicular magnetic field. It kinetic energy of all the ions is same, then (a) \(\mathrm{He}^{+}\)ions will be deflected more than those of \(\mathrm{O}^{2+}\) (b) \(\mathrm{He}^{+}\)ions will be deflected less than that of \(\mathrm{O}^{2+}\) (c) all the ions will be deflected equally (d) no ions will be deflected

The working principle of the mass spectrograph is that for a given combination of accelerating potential and magnetic field, the ion beam (with charge \(q\) and mass \(M\) ) to be collected at different positions of ion collectors will depend upon the value of (a) \(\sqrt{\frac{q}{M}}\) (b) \(\left(\frac{q}{M}\right)^{2}\) (c) \(\frac{q}{M}\) (d) \(q M\)

The mass of a proton is 1836 times that of an electron. An electron and a proton are projected into a uniform electric field in a direction perpendicular to the field with equal initial kinetic energies. Then (a) the electron trajectory is less curved than the proton trajectory (b) the proton trajectory is less curved than the electron trajectory (c) Both trajectories are equally curved (d) Both trajectories will be straight

The binding energy of the innermost electron in tungsten is \(40 \mathrm{k} \mathrm{eV}\). To produce characteristic X-rays using a tungsten target in an X-rays tube, the potential difference between the cathode and anti cathode should be (a) \(V<40 \mathrm{kV}\) (b) \(V \leq 40 \mathrm{kV}\) (c) \(V>40 \mathrm{kV}\) (d) \(V=40 \mathrm{kV}\)

An ionisation chamber, with parallel conducting plates as anode and cathodes has \(5 \times 10^{7} \mathrm{~cm}^{-3}\) electrons and the same number of singly charged positive ions per \(\mathrm{cm}^{3}\). The electrons are moving toward the anode with velocity \(0.4 \mathrm{~ms}^{-1}\). The current density from anode to cathode is \(4 \mu \mathrm{Am}^{-2}\). The velocity of positive ions moving towards cathode is (a) \(0.1 \mathrm{~ms}^{-1}\) (b) \(0.4 \mathrm{~ms}^{-1}\) (c) zero (d) \(1.6 \mathrm{~ms}^{-1}\)

An X-ray tube with copper target emit \(K_{\alpha}\) line of wavelength \(1.50 \AA\). What should be the minimum voltage through which electrons one to be accelerated to produce this wavelength of X-rays. \(\left(h=6.6 \times 10^{-34} \mathrm{Js}, c=3 \times 10^{8} \mathrm{~ms}^{-1}\right)\) (a) \(82.8 \mathrm{~V}\) (b) \(8280 \mathrm{~V}\) (c) \(82801 \mathrm{~V}\) (d) \(828 \mathrm{~V}\)

If \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelength of characteristic \(\mathrm{X}\)-rays and \(\gamma\)-rays respectively, then the relation between them is (a) \(\lambda_{1}>\lambda_{2}\) (b) \(\lambda_{1}<\lambda_{2}\) (c) \(\lambda_{1}=\lambda_{2}\) (d) \(\lambda_{1} \lambda_{2}=1\)

In an ionisation experiment it is found that a doubly fonised particle enters a magnetic field of \(1 \mathrm{~T}\) and moves in a circular path of radius \(1 \mathrm{~m}\) with a speed of \(16 \times 10^{7} \mathrm{~ms}^{-1}\). The particle must be (a) \(\mathrm{C}^{+\star}\) (b) \(\mathrm{Be}^{++}\) (c) \(\mathrm{Li}^{++}\) (d) \(\mathrm{He}^{++}\)

Consider the following statements concerning electrons I. Electrons are universal constituents of matter. II. J J Thomson received the very first Nobel prize in Physics for discovering the electron. III. The mass of the electron is about \(1 / 2000\) of a neutron. IV. According to Bohr the linear momentum of the electron is quantised in the hydrogen atom. Which of the above statements are not correct? (a) 1 (b) 1 (c) 111 (d) IV

An \(\alpha\)-particle of mass \(6.65 \times 10^{-27} \mathrm{~kg}\) travels at right angles to a magnetic field of \(0.2 \mathrm{~T}\) with a speed of \(6 \times 10^{5} \mathrm{~ms}^{-1}\). The acceleration of \(\alpha\)-particle will be (a) \(9.77 \times 10^{11} \mathrm{~ms}^{-2}\) (b) \(8.55 \times 10^{11} \mathrm{~ms}^{-2}\) (c) \(5.77 \times 10^{12} \mathrm{~ms}^{-2}\) (d) \(7.55 \times 10^{12} \mathrm{~ms}^{-2}\)

Cathode rays of velocity \(10^{6} \mathrm{~ms}^{-1}\) describe an approximate circular path of radius \(1 \mathrm{~m}\) in an electric field of \(500 \mathrm{~V} \mathrm{~cm}^{-1}\). If the velocity of cathode rays is doubled, the value of electric field needed so that the rays describe the same circular path is (a) \(1000 \mathrm{~V} \mathrm{~cm}^{-1}\) (b) \(1500 \mathrm{~V} \mathrm{~cm}^{-1}\) (c) \(2000 \mathrm{~V} \mathrm{~cm}^{-1}\) (d) \(500 \mathrm{~V} \mathrm{~cm}^{-1}\)

An oil drop carrying a charge \(q\) has a mass \(m \mathrm{~kg}\). It is falling freely in air with terminal speed \(v\). The electric field required to make, the drop move upwards with the same speed is (a) \(\frac{m g}{q}\) (b) \(\frac{2 m g}{q}\) (c) \(\frac{m g v}{q^{2}}\) (d) \(\frac{2 m g v}{q}\)

During \(X\)-ray production from coolidge tube if the current is increased, then (a) the penetration power increases (b) the penetration power decreases (c) the intensity of \(\mathrm{X}\)-rays increases (d) the intensity of \(X\)-rays decreases

When yellow light is incident on a surface, no electrons emitted while green light can emit. If red light is incident on the surface, then (a) no electrons are emitted (b) photons are emitted (c) elements of higher energy are emitted (d) elements of lower energy are emitted

A charged dust particle of radius \(5 \times 10^{-7} \mathrm{~m}\) is located in a horizontal electric field having an intensity of \(6.28 \times 10^{5} \mathrm{Vm}^{-1}\). The surrounding medium in air with coefficient of viscosity \(\eta=16 \times 10^{-15} \mathrm{Nsm}^{-2}\). If this particle moves with a uniform horizontal speed of \(0.01 \mathrm{~ms}^{-1}\), the number of electrons on it will be (a) 20 (b) 15 (c) 25 (d) 30

Two identical photo cathodes receive light of frequencies \(f_{1}\) and \(f_{2} .\) If the velocities of the photo electrons (of mass \(m\) ) coming out are respectively, \(v_{1}\) and \(v_{2}\), then (a) \(v_{1}-v_{2}=\left[\frac{2 h}{m}\left(f_{1}-f_{2}\right)\right]^{1 / 2}\) (b) \(v_{1}^{2}-v_{2}^{2}=\frac{2 h}{m}\left(f_{1}-f_{2}\right)\) (c) \(v_{1}+v_{2}=\left[\frac{2 h}{m}\left(f_{1}+f_{2}\right)\right]^{1 / 2}\) (d) \(v_{1}^{2}+v_{2}^{2}=\frac{2 h}{m}\left(f_{1}+f_{2}\right)\)

The mass of a particle is 400 times than that of an electron and the charge is double. The particle is accelerated by \(5 \mathrm{~V}\). Initially the particle remained in rest, then its final KE will be (a) \(10 \mathrm{eV}\) (b) \(5 \mathrm{eV}\) (c) \(50 \mathrm{eV}\) (d) \(100 \mathrm{eV}\)

A cathode emits \(1.8 \times 10^{14}\) electrons per second, when heated. When \(400 \mathrm{~V}\) is applied to anode all the emitted electrons reach the anode. The charge on electron is \(1.6 \times 10^{-19}\) C. One maximum anode current is (a) \(2.7 \mu \mathrm{A}\) (b) \(29 \mu \mathrm{A}\) (c) \(72 \mu \mathrm{A}\) (d) \(29 \mathrm{~mA}\)

If in a Thomson's mass spectrograph, the ratio of the electric field and magnetic field, in order to obtain concident parabola of singly ionised and doubly ionised positive ions are \(1: 2\) and \(3: 2\) respectively, then the ratio of masses of particles will be (a) \(3: 1\) (b) \(2: 1\) (c) \(9: 4\) (d) \(9: 2\)

A charged oil drop falls with terminal velocity \(v_{0}\) in the absence of electric field. An electric field \(E\) keeps it stationary. The drop acquires charge \(3 q\), it starts moving upwards with velocity \(v_{0}\). The initial charge on the drop is (a) \(\frac{q}{2}\) (b) \(q\) (c) \(\frac{3 q}{2}\) (d) \(2 q\)

The specific charge for positive rays is much less than that for cathode rays. This is because (a) masses of positive rays are much larger (b) charge on positive ray is less (c) positive rays are positively charged (d) experiment method is wrong

The filament current in the electron gun of a coolidge tube is increased while the potential difference used to accelerate the electrons is decreased. As a result, in the emitted radiation (a) the intensity increases while the minimum wavelength decreases (b) the intensity decreases while the minimum wavelength increases (c) the intensity as well as the minimum wavelength increases (d) the intensity as well as the minimum wavelength decreases

If a cathode ray tube has a potential difference \(V\) volt between the cathode and anode, then the speed \(v\) of cathode rays is given by (a) \(v \propto V^{2}\) (b) \(v \propto \sqrt{V}\) (c) \(v \propto V^{-1}\) (d) \(v \propto V\)

What is the strength of transverse magnetic field required to bend all the photoelectrons within a circle of a radius \(50 \mathrm{~cm}\). When light of wavelength \(3800 \AA\) Ais incident on a barium emitted? (Given that work function of barium is \(2.5 \mathrm{eV} ; h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}\); \(\left.e=1.6 \times 10^{-19} \mathrm{C} ; m=9.1 \times 10^{-31} \mathrm{~kg}\right)\) (a) \(6.32 \times 10^{-4} \mathrm{~T}\) (b) \(6.32 \times 10^{-5} \mathrm{~T}\) (c) \(6.32 \times 10^{-6} \mathrm{~T}\) (d) \(6.32 \times 10^{-8} \mathrm{~T}\)

An electric field of intensity \(6 \times 10^{4} \mathrm{Vm}^{-1}\) is applied perpendicular to the direction of motion of the electron. A magnetic field of induction \(8 \times 10^{-2} \mathrm{Wm}^{-2}\) is applied perpendicular to both the electric field and direction of motion of the electron. What is the velocity of the electron if it passes undeflected? (a) \(7.5 \times 10^{5} \mathrm{~ms}^{-1}\) (b) \(7.5 \times 10^{-5} \mathrm{~ms}^{-1}\) (c) \(48 \times 10^{-2} \mathrm{~ms}^{-1}\) (d) It is never possible

Given that a photon of light of wavelength \(10,000 \AA\) has an energy equal to \(1.23 \mathrm{eV}\). When light of wavelength \(5000 \AA\) And intensity \(I_{0}\) falls on a photoelectric cell, the surface current is \(0.40 \times 10^{-6} \mathrm{~A}\) and the stopping potential is \(1.36 \mathrm{~V}\), then the work function is (a) \(0.43 \mathrm{eV}\) (b) \(0.55 \mathrm{eV}\) (c) \(1.10 \mathrm{eV}\) (d) \(1.53 \mathrm{eV}\)

The mean free path of the electrons in a discharge tube is \(20 \mathrm{~cm}\). The length of the tube is \(15 \mathrm{~cm}\) only. Then length of Crooke's dark space is (a) \(5 \mathrm{~cm}\) (b) \(20 \mathrm{~cm}\) (c) \(15 \mathrm{~cm}\) (d) \(25 \mathrm{~cm}\)

Light of wavelength \(488 \mathrm{~nm}\) is produced by an argon laser, which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is \(0.38 \mathrm{~V}\). Find the work function of the material from which the emitter is made. (a) \(2.2 \mathrm{eV}\) (b) \(3.7 \mathrm{eV}\) (c) \(1.6 \mathrm{eV}\) (d) \(4.2 \mathrm{eV}\)

A nucleus \({ }_{Z} X^{A}\) emits an \(\alpha\)-particle. The resultant nucleus emits a \(\beta^{+}\)particle. The respective atomic and mass numbers of the final nucleus will be (a) \(Z-3, A-4\) (b) \(Z-1, A-4\) (c) \(Z-2, A-4\) (d) \(Z, A-2\)

A positively charged particle enters a magnetic field of value \(B \hat{j}\) with a velocity \(v \mathbf{k}\). The particle will move along (a) \(+X\)-axis (b) \(-X\)-axis (c) \(+Z\)-axis (d) \(-Z\)-axis

Two radioactive materials \(X_{1}\) and \(X_{2}\) have decay constants \(10 \lambda\) and \(\lambda\) respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of \(X_{1}\) to that of \(X_{2}\) will be \(1 / e\) after a time (a) \(\frac{1}{10 \lambda}\) (b) \(\frac{1}{11 \lambda}\) (c) \(\frac{11}{10 \lambda}\) (d) \(\frac{1}{9 \lambda}\)

In a mass spectrograph, an ion \(X\) of mass number 24 and charge \(+e\) and another ion \(Y\) of mass number 22 and charge+ \(2 e\) enter in a perpendicular magnetic field with the same velocity. The ratio of the radii of the circular path in the field will be (a) \(\frac{11}{22}\) (b) \(\frac{11}{2}\) (c) \(\frac{22}{11}\) (d) \(\frac{24}{11}\)

A beam of electrons of velocity \(3 \times 10^{7} \mathrm{~ms}^{-1}\) is deflected \(1.5 \mathrm{~mm}\) is passing \(10 \mathrm{~cm}\) through an electric field of \(1800 \mathrm{Vm}^{-1}\) perpendicular to their path. The value of \(\frac{e}{m}\) for electron is (a) \(1.78 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}\) (b) \(2 \times 10^{11} \mathrm{Ckg}^{-1}\) (c) \(1.5 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}\) (d) \(3.5 \times 10^{11} \mathrm{C} \mathrm{kg}^{-1}\)

Taking the Bohr radius as \(a_{0}=53 \mathrm{pm}\), the radius of \(\mathrm{Li}^{\text {t+ }}\) ion in its ground state, on the basis of Bohr's model, will be about \(\quad\) [NCERT Exemplar] (a) \(53 \mathrm{pm}\) (b) \(27 \mathrm{pm}\) (c) \(18 \mathrm{pm}\) (d) \(13 \mathrm{pm}\)

In a fission reaction \({ }_{92} \mathrm{U}^{236}=X^{117}+Y^{117}+n+n\), the binding energy per nucleon of \(X\) and \(Y\) is \(8.5 \mathrm{MeV}\), whereas of \(\mathrm{U}^{236}\) is \(7.6 \mathrm{MeV}\). The total energy liberated will be about (a) \(200 \mathrm{keV}\) (b) \(2 \mathrm{MeV}\) (c) \(200 \mathrm{MeV}\) (d) \(2000 \mathrm{MeV}\)

Let the PE of hydrogen atom in the ground state be zero. Then its total energy in the first excited state will be (a) \(27.2 \mathrm{eV}\) (b) \(23.8 \mathrm{eV}\) (c) \(12.6 \mathrm{eV}\) (d) \(10.2 \mathrm{eV}\)

A hydrogen atom and a \(\mathrm{Li}^{2+}\) ion are both in second excited state. If \(l_{\mathrm{H}}\) and \(l_{\mathrm{Li}}\) are their respective electronic angular momenta and \(E_{\mathrm{H}}\) and \(E_{\mathrm{Li}}\) their respective energies, then (a) \(l_{H}>I_{\mathrm{U}}\) and \(\left|E_{\mathrm{H}}\right|>\left|E_{\mathrm{L}}\right|\) (b) \(L_{\mathrm{H}}=L_{i}\) and \(\left|E_{\mathrm{H}}\right|<\left|E_{\mathrm{U}}\right|\) (c) \(l_{H}>I_{\mathrm{L}}\) and \(\left|E_{\mathrm{H}}\right|>\left|E_{\mathrm{U}}\right|\) (d) \(l_{H}>l_{\mathrm{L}}\) and \(\left|E_{\mathrm{H}}\right| \ll\left|E_{\mathrm{L} \mid}\right|\)

Ionisation energy of an electron present in the second Bohr's orbit of hydrogen is (a) \(54.4 \mathrm{eV}\) (b) \(13.6 \mathrm{eV}\) (c) \(1.5 \mathrm{eV}\) (d) \(3.4 \mathrm{eV}\)

Hydrogen atom excites energy level from fundamental state to \(n=3 .\) Number of spectrum lines, according to Bohr, is (a) 4 (b) 3 (c) 1 (d) 2

The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is \(B=\frac{m e^{4}}{8 n^{2}{\underline{\phantom{xx}}}_{0}^{2} h^{2}} \cdot(m=\) proton mass \()\) If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B=-\frac{M e^{4}}{8 n^{2} \varepsilon_{0}^{2} h^{2}}(M=\) proton mass \() .\) This last expression is not correct because (a) \(n\) would not be integral (b) Bohr-quantisation applies only to electron (c) the frame in which the electron is at rest is not inertial. (d) the motion of the proton would not be in circular orbits, even approximately.

Ionisation 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 atoms according to Bohr's theory will be (a) one (b) two (c) three (d) four

The ionization energy of hydrogen atom is \(13.6 \mathrm{eV}\). Following Bohr's theory, the energy corresponding to a transition between 3 rd and 4 th orbit is (a) \(3.40 \mathrm{eV}\) (b) \(1.51 \mathrm{eV}\) [c) \(0.85 \mathrm{eV}\) (d) \(0.66 \mathrm{eV}\)

The ionization energy of hydrogen atom is \(13.6 \mathrm{eV}\). Following Bohr's theory, the energy corresponding to a transition between 3 rd and 4 th orbit is (a) \(3.40 \mathrm{eV}\) (b) \(1.51 \mathrm{eV}\) [c) \(0.85 \mathrm{eV}\) (d) \(0.66 \mathrm{eV}\)

An ionised H-molecule consist of an electron and two protons. One proton are separated by a small distance of the order of angstrom. In the ground state (a) the electron would not move in circular orbits (b) the energy would be \((z)^{4}\) times that of a \(\mathrm{H}\)-atom (c) the molecule will soon decay in the proton and a H-atom (d) None of the above

A sample of an element is \(10.38 \mathrm{~g}\). If half-life of element is \(3.8\) days, then after 19 days, how much quantity of element remains? (a) \(0.151 \mathrm{~g}\) (b) \(0.32 \mathrm{~g}\) (c) \(1.51 \mathrm{q}\) (d) \(0.16 \mathrm{q}\)

In \(\mathrm{H}\) spectrum, the wavelength of \(\mathrm{H}_{\alpha}\) line is \(656 \mathrm{~nm}\) whereas in a distance galaxy, the wavelength of \(\mathrm{H}_{\alpha}\) line is \(706 \mathrm{~nm}\). Estimate the speed of galaxy with respect to earth. (a) \(2 \times 10^{8} \mathrm{~ms}^{-1}\) (b) \(2 \times 10^{7} \mathrm{~ms}^{-1}\) (c) \(2 \times 10^{6} \mathrm{~ms}^{-1}\) (d) \(2 \times 10^{5} \mathrm{~ms}^{-1}\)

If the shortest wavelength in the Lyman series is \(911.6 \AA\), the longest wavelength in the same series will be (a) \(1600 \mathrm{~A}\) (b) \(2430 \mathrm{~A}\) (c) \(1215 \mathrm{~A}\) (d) \(\infty\)

The radioactivity of a given sample of whisky due to tritium (half-life \(12.3 \mathrm{yr}\) ) was found to be only \(3 \%\) of that measured in a recently purchased bottle marked 7 years old. The sample must have been prepared about (a) 220 years back (b) 300 years back (c) 400 years back (d) 70 years back