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Questions:

Multiple Choice Question

15 x 1 = 15

Emission of electrons by the absorption of heat energy is called ______ emission.

(a)

photoelectric

(b)

field

(c)

thermionic

(d)

secondary

The work functions for metals A, B and C are 1.92 eV, 2.0 eV and 5.0 eV respectively. The metal/metals which will emit photoelectrons for a radiation of wavelength 4100 Å is/are _____.

(a)

A only

(b)

both A and B

(c)

all these metals

(d)

none

Photons of wavelength λ are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a perpendicular magnetic field having magnitude B. The work function of the metal is _____.

(a)

\(\frac { hc }{ \lambda } -{ m }_{ e }+\frac { e^{ 2 }{ B }^{ 2 }{ R }^{ 2 } }{ { 2m }_{ e } } \)

(b)

\(\frac { hc }{ \lambda } +{ 2m }_{ e }{ \left[ \frac { eBR }{ { 2m }_{ e } } \right] }^{ 2 }\)

(c)

\(\\ \frac { hc }{ \lambda } -{ m }_{ e }{ c }^{ 2 }-\frac { e^{ 2 }{ B }^{ 2 }{ R }^{ 2 } }{ { 2m }_{ e } } \)

(d)

\(\frac { hc }{ \lambda } -{ 2m }_{ e }{ \left[ \frac { eBR }{ { 2m }_{ e } } \right] }^{ 2 }\)

A light of wavelength 500 nm is incident on a sensitive metal plate of photoelectric work function 1.235 eV. The kinetic energy of the photoelectrons emitted is_____. (Take h = 6.6 x 10^–34Js)

(a)

0.58 eV

(b)

2.48 eV

(c)

1.24 eV

(d)

1.16 eV

The threshold wavelength for a metal surface whose photoelectric work function is 3.313 eV is _____.

(a)

4125 \(\mathring { A } \)

(b)

3750\(\mathring { A } \)

(c)

6000\(\mathring { A } \)

(d)

2062.5\(\mathring { A } \)

If the mean wavelength of light from sun is taken as 550 nm and its mean power as 3.8 x 10²⁶W, then the number of photons emitted per second from the sun is of the order of _____.

(a)

10⁴⁵

(b)

10⁴²

(c)

10⁵⁴

(d)

10⁵¹

A light source of wavelength 520 nm emits 1.04 x 10¹⁵photons per second while the second source of 460 nm produces 1.38 x 10¹⁵ photons per second. Then the ratio of power of second source to that of first source is _____.

(a)

1.00

(b)

1.02

(c)

1.5

(d)

0.98

Two radiations with photon energies 0.9 eV and 3.3 eV respectively are falling on a metallic surface successively. If the work function of the metal is 0.6 eV, then the ratio of maximum speeds of emitted electrons in the two cases will be _____.

(a)

1:4

(b)

1:3

(c)

1:1

(d)

1:9

In photoelectric emission, a radiation whose frequency is 4 times threshold frequency of a certain metal is incident on the metal. Then the maximum possible velocity of the emitted electron will be _____.

(a)

\(\sqrt { \frac { { hv }_{ o } }{ m } } \)

(b)

\(\sqrt { \frac { { 6hv }_{ o } }{ m } } \)

(c)

\(2\sqrt { \frac { { hv }_{ o } }{ m } } \)

(d)

\(\sqrt { \frac { { hv }_{ o } }{2m } } \)

10.

A photoelectric surface is illuminated successively by monochromatic light of wavelength λ and λ /2. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the material is _____.

(a)

\(\frac{hc}{\lambda}\)

(b)

\(\frac{2hc}{\lambda}\)

(c)

\(\frac{hc}{3\lambda}\)

(d)

\(\frac{hc}{2\lambda}\)

11.

If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the electrons are emitted. Then the wavelength of the wave associated with the emitted electron is _____.(Take h = 6.6 x 10^–34 Js)

(a)

< 2.75 ×10⁻⁹m

(b)

≥ 2.75 × 10⁻⁹m

(c)

≤ 2.75 × 10⁻¹²m

(d)

< 2.5 × 10⁻¹⁰m

12.

When a metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential is \(\frac{V}{4}\). The threshold wavelength for the metallic surface is _____.

(a)

4λ

(b)

5λ

(c)

\(\frac{5}{2}λ\)

(d)

3λ

13.

The wave associated with a moving particle of mass 3 x 10^–6 g has the same wavelength as an electron moving with a velocity 6 x 10⁶ ms^-1. The velocity of the particle is _____.

(a)

1.82 x 10^-18ms^-1

(b)

9 x 10^-2ms^-1

(c)

3 x 10^-31ms^-1

(d)

1.82 x 10^-15ms^-1

14.

In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the voltage is changed to 224 kV, then the de Broglie wavelength associated with the electrons would _____.

(a)

increase by 2 times

(b)

decrease by 2 times

(c)

decrease by 4 times

(d)

increase by 4 times

15.

The wavelength λ_eof an electron and λ_p of a photon of same energy E are related by _____.

(a)

λ_p ∝ λ_e

(b)

\({ \lambda }_{ p }∝ \sqrt { { \lambda }_{ e } } \)

(c)

\({ \lambda }_{ p }∝ \frac { 1 }{ \sqrt { { \lambda }_{ e } } } \)

(d)

\({ \lambda }_{ p }∝ { \lambda }_{ e }^{ 2 }\)

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Answers Key:

Multiple Choice Question

15 x 1 = 15

\(E=\frac{12400 \stackrel{o}A}{4100 \stackrel{o}A}=3.02 eV\)

\(\text {K.E } =\frac{B^2 q^2 r^2}{2 m} \)
\(\phi =\frac{h c}{\lambda}-K . E \)
\(=\frac{h c}{\lambda}-\frac{B^2 q^2 r^2}{2 m} \)
\(\phi =\frac{h c}{\lambda}-2 m\left(\frac{B q r}{2 m}\right)^2\)

\(K .E_{\max } =\mathrm{hv}-\phi \)
\(=\frac{\mathrm{hc}}{\lambda}-\phi \)
\(\mathrm{E} =\frac{6.6 \times 10^{-34} \times 3 \times 10^8-1.235}{500 \times 10^{-9} \times 1.6 \times 10^{-19}} \)
\(=2.475-1.235 \)
\(\text {K. } \mathrm{E}_{\max } =1.24 \mathrm{eV}\)

\(\lambda_0 =\frac{h c}{\phi} \)
\(=\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{3.313 \times 1.6 \times 10^{-19}} \)
\( =\frac{19.8782400}{5.3} \times 10^{-7} \)
\(\lambda_0 =3.750 \times 10^{-7} \simeq 3750 \stackrel{o}A\)

\(\mathrm{P} =\frac{\mathrm{n}}{\mathrm{t}} \frac{\mathrm{hc}}{\lambda} \)
\(\frac{\mathrm{n}}{\mathrm{t}} =\frac{\mathrm{P} \lambda}{\mathrm{hc}} \)
\(\frac{\mathrm{n}}{\mathrm{t}} =\frac{3.8 \times 10^{26} \times 550 \times 10^{-9}}{6.6 \times 10^{-3} \times 3 \times 10^8}=1 \times 10^{-15}\)

\(P =\frac{E}{t}=\frac{n h v}{t}=\frac{n h c}{\lambda t} \Rightarrow P \propto n / t \)
\(\frac{P_1}{P_2} =\frac{1.38 \times 10^{15}}{460} \times \frac{520}{1.04 \times 10^{15}}=1.5\)

K.E= hv - Φ
K.E₁ = 0.9 - 0.6 = 0.3 eV
K.E₂ = 3.3 - 0.6 = 2.7 ev
K.E ∝ v²
\(\frac{0.3}{2.7}=\frac{v^2_1}{v^2_2} \)
\(\frac{v^1}{v^2} =\frac{1}{3}\)

(b)
\(\sqrt { \frac { { 6hv }_{ o } }{ m } } \)

10.

\(\frac{\mathrm{hc}}{\lambda} =\phi+\mathrm{K} . \mathrm{E} .....(1) \)
\(\frac{2 \mathrm{hc}}{\lambda} =\phi+3 \mathrm{~K} . \mathrm{E}......(2)\)
multiply eqn. (1) by 3, we get
\(\frac{3 \mathrm{hc}}{\lambda} =3\phi+3 \mathrm{~K} . \mathrm{E} .....(3)\)
Subtract eqn. (2) from (3), we get
\(\frac{\mathrm{hc}}{\lambda} =2\phi \)
\(\phi=\frac{ \mathrm{hc}}{2\lambda} \)

11.

(b)
≥ 2.75 × 10⁻⁹m

12.

\(\frac{\mathrm{hc}}{\lambda}=\phi+\mathrm{eV} \) .....(1)
\(\frac{\mathrm{hc}}{2 \lambda}=\phi+\frac{\mathrm{eV}}{4}\) .....(2)
multiply (2) eqn by 4
\(\frac{2 h c}{\lambda}=4 \phi+\mathrm{eV}\) .....(3)
subtract eqn (1) from (3), we get
\(\frac{ h c}{\lambda}=3 \phi \Rightarrow \phi = \frac{ h c}{3\lambda}\)
\(\frac{ h c}{\lambda_o}=\frac{ h c}{3\lambda}\)
⋋_o = 3⋋

13.

\(\lambda_{\mathrm{i}} \frac{1}{\mathrm{mv}} \)
\(\frac{\lambda_p}{\lambda_e} =\frac{m_e v_e}{m_P v_P} \)
\(1 =\frac{9.1 \times 10^{-31} \times 6 \times 10^6}{3 \times 10^{-9} \times v_p} \)
\(\mathrm{v}_{\mathrm{p}} =9.1 \times 10^{-16} \times 2 \)
\(\mathrm{v}_{\mathrm{p}} =18.2 \times 10^{-16} \)
\(\mathrm{v}_{\mathrm{p}} =1.82 \times 10^{-15} \mathrm{~m} \mathrm{~s}^{-1}\)

14.

\(\lambda\propto \frac{1}{\sqrt{V}}\)
\(\frac{\lambda_1}{\lambda_2}=\frac{\sqrt{224\times10^3}}{\sqrt{14\times 10^3}}\)
\(=\sqrt{16}=4\)
\(\lambda_{\mathrm{2}}= \frac{\lambda_1}{4}\)

15.

\(\mathrm{E}_{\mathrm{p}} =\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}} \)
\(\mathrm{E}_{\mathrm{e}} =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2} \)
\(\frac{\mathrm{hc}}{\lambda_{\mathrm{p}}} =\frac{\mathrm{h}^2}{2 \mathrm{~m} \lambda_{\mathrm{e}}^2} \)
\(\lambda_{\mathrm{p}} \propto \lambda_{\mathrm{e}}^{{ }^2}\)