Chapter 25

A parallel beam of light is incident normally on a plane surface absorbing \(40 \%\) of the light and reflecting the rest. If the incident beam carries \(60 \mathrm{~W}\) of power, the force exerted by it on the surface is (a) \(3.2 \times 10^{-8} \mathrm{~N}\) (b) \(3.2 \times 10^{-7} \mathrm{~N}\) (c) \(5.12 \times 10^{-7} \mathrm{~N}\) (d) \(5.12 \times 10^{-8} \mathrm{~N}\)

In a photoelectric experiment for 4000 \AA incident radiation. The potential difference to stop the ejection is \(2 \mathrm{~V}\). If the incident light is changed to \(3000 \AA\), then the potential required to stop the ejection of electrons will be (a) greater than \(2 \mathrm{~V}\) (b) less than \(2 \mathrm{~V}\) (c) \(\infty\) (d) zero

Calculate the energy of a photon with momentum \(3.3 \times 10^{-13} \mathrm{~kg}-\mathrm{ms}^{-1}\), given Planck's constant to be \(6.6 \times 10^{-34} \mathrm{Js}\) (a) \(7.3 \times 10^{4} \mathrm{~J}\) (b) \(9.9 \times 10^{-5} \mathrm{~J}\) (c) \(1.3 \times 10^{5} \mathrm{~J}\) (d) \(8.1 \times 10^{3} \mathrm{~J}\)

An electron and a proton have the same de-Broglie wavelength. Then the kinetic energy of the electron is (a) zero (b) infinity (c) equal to kinetic energy of the proton (d) greater than the kinetic energy of proton

A particle of mass \(1 \mathrm{mg}\) has the same wavelength as an electron moving with a velocity of \(3 \times 10^{6} \mathrm{~ms}^{-1}\). The velocity of the particle is (a) \(3 \times 10^{-31} \mathrm{~ms}^{-1}\) (b) \(2.7 \times 10^{-21} \mathrm{~ms}^{-1}\) (c) \(2.7 \times 10^{-18} \mathrm{~ms}^{-1}\) (d) \(9 \times 10^{-2} \mathrm{~ms}^{-1}\)

Energy required to remove an electron from an aluminium surface is \(4.2 \mathrm{eV}\). If light of wavelength \(2000 \AA\) falls on the surface, the velocity of fastest electrons ejected from the surface is (a) \(2.5 \times 10^{18} \mathrm{~ms}^{-1}\) (b) \(2.5 \times 10^{13} \mathrm{~ms}^{-1}\) (c) \(6.7 \times 10^{18} \mathrm{~ms}^{-1}\) (d) None of the above

The energy that should be added to an electron to reduce its de-Broglie wavelength from \(10^{-10} \mathrm{~m}\) to \(0.5 \times 10^{-10} \mathrm{~m}\), will be (a) four times the initial energy (b) thrice the initial energy (c) equal to the initial energy (d) twice the initial energy

The maximum wavelength of radiation that can produce photoelectric effect in certain metal is \(200 \mathrm{~nm} .\) The maximum kinetic energy acquired by electron due to radiation of wavelength \(100 \mathrm{~nm}\) will be (a) \(12.4 \mathrm{eV}\) (b) \(6.2 \mathrm{eV}\) (c) \(100 \mathrm{eV}\) (d) \(200 \mathrm{eV}\)

The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with \(1 \mathrm{MeV}\) energy is nearly (a) \(1.2 \mathrm{~nm}\) (b) \(1.2 \times 10^{-3} \mathrm{~nm}\) (c) \(1.2 \times 10^{-6} \mathrm{~nm}\) (d) \(1.2 \times 10^{1} \mathrm{~nm}\)

What is the de-Broglie wavelength (in \(\AA\) ) of the \(\alpha\)-particle accelerated through a potential difference \(V ?\) (a) \(\frac{0.287}{\sqrt{V}}\) (b) \(\frac{12.27}{\sqrt{V}}\) (c) \(\frac{0.101}{\sqrt{V}}\) (d) \(\frac{0.22}{\sqrt{v}}\)

Photons absorbed in matter are converted to heat. A source emitting \(n\) photon/sec of frequency \(v\) is used to converting of ice at \(0^{\circ} \mathrm{C}\) to water at \(0^{\circ} \mathrm{C}\). Then, the time, \(T\) taken for the conversion (a) decreases with increasing \(n\), with \(v\) fixed (b) decreases with \(n\) fixed, \(v\) increasing (c) remains constant with \(n\) and \(v\) changing such that \(n v=\) constant (d) increases when the product \(n \underline{v}\) increases

There are two sources of light each emitting with a power of \(100 \mathrm{~W}\). One emits X-rays of wavelength \(1 \mathrm{~nm}\) and the other visible light of wavelength \(500 \mathrm{~nm} .\) Find the ratio of number of photons of X-rays in the photons of visible light of the given wavelength? (a) \(1: 500\) (b) \(1: 250\) (c) \(1: 20\) (d) 100

Maximum velocity of photoelectron emitted is \(4.8 \mathrm{~ms}^{-1}\). The \(\frac{e}{m}\) ratio of electron is \(1.76 \times 10^{11} \mathrm{Ckg}^{-1}\), then stopping potential is given by (a) \(5 \times 10^{-10} \mathrm{JC}^{-1}\) (b) \(3 \times 10^{-7} \mathrm{JC}^{-1}\) (c) \(7 \times 10^{11} \mathrm{JC}^{-1}\) (d) \(2.5 \times 10^{-2} \mathrm{JC}^{-1}\)

Consider a metal exposed to light of wavelength \(600 \mathrm{~nm}\). The maximum energy of the electron doubles when light of wavelength \(400 \mathrm{~nm}\) is used. The work function in eV is \(\quad\) [NCERT Exemplar] (a) \(1.50 \mathrm{eV}\) (b) \(1.02 \mathrm{eV}\) (c) \(1.94 \mathrm{eV}\) (d) \(2.76 \mathrm{eV}\)

An important spectral emission line has a wavelength of \(21 \mathrm{~cm}\). The corresponding photon energy is \(\left(h=6.62 \times 10^{-34}\right.\) \(\begin{array}{ll}\text { (a) } 5.9 \times 10^{-8} \mathrm{eV} & \text { (b) } 5.9 \times 10^{-4} \mathrm{eV}\end{array}\) (c) \(5.9 \times 10^{-6} \mathrm{eV}\) (d) \(11.8 \times 10^{-6} \mathrm{eV}\)

A proton and an \(\alpha\)-particle are accelerated through the same potential difference. The ratio of their de-Broglie wavelengths, \(\left(\frac{\lambda_{p}}{\lambda_{\alpha}}\right)\) is (a) \(\frac{1}{2 \sqrt{2}}\) (b) \(\underline{1}\) (c) 2 (d) \(2 \sqrt{2}\)

The energy of a photon of green light of wavelength \(50000 \mathrm{~A}\) is (a) \(3.459 \times 10^{-19} \mathrm{~J}\) (b) \(3.973 \times 10^{-19} \mathrm{~J}\) (c) \(4.132 \times 10^{-19} \mathrm{~J}\) (d) \(8453 \times 10^{-19} \mathrm{~J}\)

The de-Broglie wavelength of a neutron at \(27^{\circ} \mathrm{C}\) is \(\lambda_{0}\). What will be its wavelength at \(927^{\circ} \mathrm{C}\) ? (a) \(\lambda / 4\) (b) \(\lambda / 3\) (c) \(\lambda / 2\) (d) \(3 \lambda / 2\)

What will be the number of photons emitted per second by a \(10 \mathrm{~W}\) sodium vapour lamp assuming that \(90 \%\) of the consumed energy is converted into light? [Wavelength of sodium light is \(590 \quad \mathrm{~nm}\), \(\left.h=6.63 \times 10^{-34} \mathrm{~J}_{-\mathrm{s}}\right]\) \(\begin{array}{ll}\text { (a) } 0.267 \times 10^{18} & \text { (b) } 0.267 \times 10^{19}\end{array}\) (c) \(0.267 \times 10^{20}\) (d) \(0.267 \times 10^{17}\)

An electron of mass \(m\) when accelerated through a potential difference has de-Broglie wavelength \(\lambda\). The de-Broglie wavelength associated with a proton of mass \(M\) accelerated through the same potential difference will be (b) \(\lambda \sqrt{\frac{m}{M}}\) (a) \(\lambda \frac{m}{M}\) (c) \(\lambda \frac{M}{m}\) (d) \(\lambda \sqrt{\frac{M}{m}}\)

If the energy of photons corresponding to the wavelength of \(6000 \mathrm{~A}\) is \(3.2 \times 10^{-19} \mathrm{~J}\), the photon energy for a wavelength of 4000 A will be (a) \(1.11 \times 10^{-19} \mathrm{~J}\) (b) \(2.22 \times 10^{-19} \mathrm{~J}\) (c) \(4.40 \times 10^{-19} \mathrm{~J}\) (d) \(4.80 \times 10^{-19} \mathrm{~J}\)

A \(100 \mathrm{~W}\) sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is \(589 \mathrm{~nm} .\) (i) What is the energy per photon associated with the sodium light? (ii) At what rate are the photons delivered to the sphere? (a) (i) \(4.6 \mathrm{eV}\) (ii) \(1.6 \times 10^{24}\) photon/s (b) (i) \(3.4 \mathrm{eV}\) (ii) \(4.5 \times 10^{24}\) photon/s (c) (i) \(2.1 \mathrm{eV}\) (ii) \(3 \times 10^{20}\) photon/s (d) (i) \(1.1 \mathrm{eV}\) (ii) \(2 \times 10^{24}\) photon/s

A radio transmitter operates at a frequency \(880 \mathrm{kHz}\) and a power of \(10 \mathrm{~kW}\). The number of photons emitted per second is (a) \(1.72 \times 10^{31}\) (b) \(1.327 \times 10^{25}\) (c) \(1.327 \times 10^{37}\) (d) \(1.327 \times 10^{45}\)

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 photoelectric threshold of Tungsten is \(2300 \AA\). The energy of the electrons ejected from the surface by ultraviolet light of wavelength \(1800 \mathrm{~A}\) is \(\left(h=6.6 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\) (a) \(0.15 \mathrm{eV}\) (b) \(1.5 \mathrm{eV}\) (c) \(15 \mathrm{eV}\) (d) \(150 \mathrm{eV}\)

A photon and electron have same de-Broglie wavelength. Give that \(v\) is the speed of electron and \(c\) is the velocity of light. \(E_{e}, E_{p}\) are the kinetic energy of electron and photon respectively. \(p_{e}, p_{h}\) are the momentum of electron and photon respectively. Then which of the following relation is correct? (a) \(\frac{E_{c}}{E_{p}}=\frac{v}{2 c}\) (b) \(\frac{E_{c}}{E_{p}}=\frac{2 c}{v}\) (c) \(\frac{p_{e}}{p_{h}}=\frac{c}{2 v}\) (d) \(\frac{p_{c}}{p_{h}}=\frac{2 c}{v}\)

Which one of the following statements regarding photo-emission of electrons is correct? (a) Kinetic energy of electrons increases with the intensity of incident light (b) Electrons are emitted when the wavelength of the incident light is above a certain threshold wavelength (c) Photoelectric emission is instantaneous with the incidence of light (d) Photo electrons are emitted whenever a gas is irradiated with ultraviolet light

Ultraviolet radiation of \(6.2 \mathrm{eV}\) falls on an aluminium surface (work function \(4.2 \mathrm{eV}\) ). The kinetic energy in joule of the fastest electron emitted is approximately. (a) \(3 \times 10^{-21}\) (b) \(3.2 \times 10^{-19}\) (c) \(3 \times 10^{-17}\) (d) \(3 \times 10^{-15}\)

A \(100 \mathrm{~W}\) light bulb is placed at the centre of a spherical chamber of radius \(0.10 \mathrm{~m} .\) Assume that \(66 \%\) of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is (a) \(0.87 \times 10^{-6} \mathrm{~Pa}\) (b) \(1.77 \times 10^{-6} \mathrm{~Pa}\) (c) \(3.50 \times 10^{-6} \mathrm{~Pa}\) (d) None of the above

Radiations of two photon's energy, twice and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of photoelectrons emitted in two cases is (a) \(1: 2\) (b) \(1: 3\) (c) \(1: 4\) (d) \(1: 1\)

A proton, a neutron, an electron and an \(\alpha\)-particle have same energy. Then their de-Broglie wavelengths compare as [NCERT Exemplar] (a) \(\lambda_{\mathrm{p}}=\lambda_{\mathrm{n}}>\lambda_{\mathrm{e}}>\lambda_{\alpha}\) (b) \(\lambda_{\alpha}=\lambda_{\mathrm{p}}>\lambda_{\mathrm{n}}>\lambda_{e}\) (c) \(\lambda_{e}=\lambda_{\mathrm{p}}>\lambda_{\mathrm{n}}>\lambda_{\alpha}\) (d) \(\lambda_{e}=\lambda_{p}>\lambda_{n}>\lambda_{a}\)

The work function for a certain metal is \(4.2 \mathrm{eV}\). Will this metal give photoelectric emission for incident radiation of wavelength \(330 \mathrm{~nm} ?\) (a) Yes (b) No (c) Cannot be said (d) may be yes or no

For a certain metal, \(v=2 v_{0}\) and the electrons come out with a maximum velocity of \(4 \times 10^{6} \mathrm{~ms}^{-1}\). If the value of \(v=5 v_{0}\), then maximum velocity of photelectrons will be (a) \(2 \times 10^{7} \mathrm{~ms}^{-1}\) (b) \(8 \times 10^{6} \mathrm{~ms}^{-1}\) (c) \(2 \times 10^{6} \mathrm{~ms}^{-1}\) (d) \(8 \times 10^{5} \mathrm{~ms}^{-1}\)

The wavelength of the photoelectric threshold for silver is \(\lambda_{0}\). The energy of the electron ejected from the surface of silver by an incident light of wavelength \(\lambda\left(\lambda<\lambda_{0}\right)\) will be (a) \(h c\left(\lambda_{0}-\lambda\right)\) (b) \(\frac{h c}{\lambda_{0}-\lambda}\) (c) \(\frac{h}{c}\left(\frac{1}{\lambda}-\frac{1}{\lambda_{0}}\right)\) (d) \(h c\left(\frac{\lambda_{0}-\lambda}{\lambda_{0} \lambda}\right)\)

In a photoelectric experiment, the wavelength of the incident light is decreased from \(6000 \AA\) to \(4000 \AA\), while the intensity of radiation remains the same (a) the cut-off potential will increase (b) the cut-off potential will decrease (c) the KE of the emitted photoelectron will increase (d) the photoelectric current will increase

A metal surface is illuminated by a light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one-fourth of its original value, then the maximum kinetic energy of the emitted photoelectrons would become (a) four times the original value (b) twice the original value (c) \(1 / 6 \mathrm{th}\) of the original value (d) unchanged

Light of frequency \(7.21 \times 10^{14} \mathrm{~Hz}\) is incident on a metal surface. Electrons with a maximum speed of \(6.0 \times 10^{5} \mathrm{~m} / \mathrm{s}\) are ejected from the surface. What is the threshold frequency for photoemission of electrons? (a) \(4.74 \times 10^{14} \mathrm{~Hz}\) (b) \(3.74 \times 10^{9} \mathrm{~Hz}\) (c) \(2.74 \times 10^{11} \mathrm{~Hz}\) (d) \(5.74 \times 10^{13} \mathrm{~Hz}\)

The work function of a metal is \(1 \mathrm{eV}\). Light of wavelength \(3000 \AA\) is incident on this metal surface. The velocity of emitted photoelectrons will be (a) \(10 \mathrm{~ms}^{-1}\) (b) \(10^{3} \mathrm{~ms}^{-1}\) (c) \(10^{4} \mathrm{~ms}^{-1}\) (d) \(10^{6} \mathrm{~ms}^{-1}\)

Two particles \(A_{1 s}\) and \(A_{2}\) of masses \(m_{1}, m_{2}\left(m_{1}>m_{2}\right)\) have the same de-broglie wavelength. Then [NCERT Exemplar] (a) their momenta are the same (b) their energies are the same (c) energy of \(A_{1}\) is less than the energy of \(A_{2}\) (d) energy of \(A_{1}\) is more than the energy of \(A_{2}\)

In the photoelectric effect, the velocity of ejected electrons depends upon the nature of the target and (a) the frequency of the incident light (b) the polarisation of the incident light (c) the time for which the light has been incident (d) the intensity of the incident light

In which of the following situations are heavier of the two particles has smaller de-Broglie wavelength? The two particles (a) move with same speed (b) move with same \(\mathrm{KE}\) (c) move with same linear momentum (d) have fallen through the same height

A photon of energy \(3.4 \mathrm{eV}\) is incident on a metal having work function \(2 \mathrm{eV}\). The maximum KE of photoelectrons is equal to (a) \(1.4 \mathrm{eV}\) (b) \(1.7 \mathrm{eV}\) (c) \(5.4 \mathrm{eV}\) (d) \(6.8 \mathrm{eV}\)

When photons of energy \(4.25 \mathrm{eV}\) strike the surface of a metal, the ejected photelectrons have a maximum kinetic energy \(E_{A} \mathrm{eV}\) and de-Broglie wavelength \(\lambda_{A}\). The maximum kinetic energy of photoelectrons liberated from another metal \(B\) by photons of energy \(4.70 \mathrm{eV}\) is \(E_{B}=\left(E_{A}-150\right) \mathrm{eV}\). If the de-Broglie wavelength of these photelectrons is \(\lambda_{B}=2 \lambda_{A}\), then (a) the work function of \(A\) is \(2.25 \mathrm{eV}\) (b) the work function of \(B\) is \(4.20 \mathrm{eV}\) (c) \(E_{A}=2.0 \mathrm{eV}\) (d) \(E_{B}=2.75 \mathrm{eV}\)

When photon of energy \(4.0 \mathrm{eV}\) strikes the surface of a metal \(A\), the ejected photoelectrons have maximum kinetic energy \(T_{A} \mathrm{eV}\) and de-Broglie wavelength \(\lambda_{A}\) The maximum kinetic energy of photoelectrons liberated from another metal \(B\) by photon of energy \(4.50 \mathrm{eV}\) is \(T_{B}=\left(T_{A}-150\right) \mathrm{eV}\). If the de-Broglie wavelength of these photoelectrons \(\lambda_{B}=2 \lambda_{A}\), then (a) the work function of \(A\) is \(1.50 \mathrm{eV}\) (b) the work function of \(B\) is \(4.0 \mathrm{eV}\) (c) \(T_{A}=2.00 \mathrm{eV}\) (d) All of the above

A metal surface of work function \(1.07 \mathrm{eV}\) is irradiated with light of wavelength \(332 \mathrm{~nm}\). The retarding potential required to stop the escape of photoelectrons is (a) \(1.07 \mathrm{eV}\) (b) \(2.66 \mathrm{eV}\) (c) \(3.7 \mathrm{eV}\) (d) \(4.81 \mathrm{eV}\)

If the work function for a certain metal is \(3.2 \times 10^{-19} \mathrm{~J}\) and it is illuminated with light of frequency \(\mathrm{v}=8 \times 10^{14} \mathrm{~Hz}\), the maximum kinetic energy of the photoelectron would be (a) \(2.1 \times 10^{-19} \mathrm{~J}\) (b) \(3.2 \times 10^{-19} \mathrm{~J}\) (c) \(5.3 \times 10^{-19} \mathrm{~J}\) (d) \(8.5 \times 10^{-19} \mathrm{~J}\)

Ultraviolet light of wavelength \(300 \mathrm{~nm}\) and intensity \(1.0 \mathrm{Wm}^{-2}\) falls on the surface of a photosensitive material. If one percent of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of \(1.0 \mathrm{~cm}^{2}\) of the surface is nearly (a) \(9.61 \times 10^{14} \mathrm{~s}^{-}\) (b) \(4.12 \times 10^{13} \mathrm{~s}^{-1}\) (c) \(1.51 \times 10^{12} \mathrm{~s}^{-1}\) (d) \(2.13 \times 10^{11} \mathrm{~s}^{-1}\)

An electron is accelerated under a potential difference of \(64 \mathrm{~V}\), the de-Broglie wavelength associated with electron is (use charge of electron \(1.6 \times 10^{-19} \mathrm{C}\), mass of electron \(9.1 \times 10^{-31} \mathrm{~kg}\) \(\left.h=6.623 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)\) (a) \(1.53 \mathrm{~A}\) (b) \(2.53 \mathrm{~A}\) (c) \(3.35 \mathrm{~A}\) (d) \(4.54 \mathrm{~A}\)

If \(\alpha\)-particle and proton have same momenta, the ratio of de-Broglie wavelength of \(\alpha\)-particle and proton is (a) 2 (b) 1 (c) \(1 / 2\) (d) \(1 / 4\)

Light of wavelength 4000 A incident on a sodium surface for which the threshold wavelength of photoelectrons is \(5420 \mathrm{~A}\). The work function of sodium is (a) \(0.57 \mathrm{eV}\) (b) \(1.14 \mathrm{eV}\) (c) \(2.29 \mathrm{eV}\) (d) \(4.58 \mathrm{eV}\)