Dual Nature Of Radiation And Matter | Physics JEE previous year questions with Solutions

Q 11 :

A metallic surface is illuminated with radiation of wavelength $λ$ , the stopping potential is $V_{0}$ . If the same surface is illuminated with radiation of wavelength $2 λ$ , the stopping potential becomes $\frac{V_{0}}{4}$ . The threshold wavelength for this metallic surface will be [2023]

$\frac{λ}{4}$
$4 λ$
$\frac{3}{2} λ$
$3 λ$

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(4)

$From the equation of photoelectric effect$

$e V_{0} = \frac{h c}{λ} - ϕ_{0} = \frac{h c}{λ} - \frac{h c}{λ_{0}}$

$\frac{e V_{0}}{4} = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$

$\Rightarrow \frac{1}{4} (\frac{h c}{λ} - \frac{h c}{λ_{0}}) = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$

$\frac{1}{λ_{0}} - \frac{1}{4 λ_{0}} = \frac{1}{2 λ} - \frac{1}{4 λ}$

$\frac{3}{4 λ_{0}} = \frac{1}{4 λ} \Rightarrow λ_{0} = 3 λ$

Q 12 :

The difference between threshold wavelengths for two metal surfaces A and B having work function $ϕ_{A} = 9 eV$ and $ϕ_{B} = 4.5 eV$ in nm is: (Given, $h c = 1242 eV nm$ ) [2023]

264
138
276
540

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(2)

$λ_{A} = (\frac{1242}{9}) = 138 nm$

$λ_{B} = (\frac{1242}{4.5}) = 276 nm$

$λ_{B} - λ_{A} = 138 nm$

Q 13 :

Given below are two statements: [2023]

Statement I: Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.

Statement II: Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.

In the light of above statements, choose the correct answer from the options given below:

Statement I is true but Statement II is false
Both Statement I and Statement II are true
Statement I is false but Statement II is true
Both Statement I and Statement II are false

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(1)

UV rays have maximum frequency hence are most effective for emission of electrons from a metallic surface.

$K E_{\max} = h f - h f_{0}$

Q 14 :

A light wave described by $E = 60 [\sin (3 \times 10^{15}) t + \sin (12 \times 10^{15}) t]$ (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately) ______ eV. $(h = 6.6 \times 10^{- 34} J·s and e = 1.6 \times 10^{- 19} C)$ [2026]

7.8
3.8
5.1
6.0

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(3)

$ω_{1} = 3 \times 10^{15} rad/sec$

$ω_{2} = 12 \times 10^{15} rad/sec$

$∵ ν = \frac{ω}{2 π}$

$E_{photon} = h ν = 6.6 \times 10^{- 34} \times 1.91 \times 10^{15}$

$= 1.26 \times 10^{- 18} J$

$E_{\max} = \frac{1.26 \times 10^{- 18}}{1.6 \times 10^{- 19}} \approx 7.9 eV$

$K_{\max} = E_{\max} - ϕ_{0}$

$= 7.9 - 2.8$

$K_{\max} = 5.1 eV$

Q 15 :

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V. If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V. The wavelength of first light is _______ m.

$(h = 6.63 \times 10^{- 34} J s, e = 1.6 \times 10^{- 19} C, c = 3 \times 10^{8} m/s)$ [2026]

$2.2 \times 10^{- 8}$
$3.1 \times 10^{- 7}$
$2.9 \times 10^{- 8}$
$2.5 \times 10^{- 7}$

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(4)

$q (3.2) = \frac{h c}{λ} - ϕ \dots (1)$

$q (0.7) = \frac{h c}{2 λ} - ϕ \dots (2)$

$Eq. (1) - Eq. (2)$

$q (2.5) = \frac{h c}{2 λ}$

$2.5 = (\frac{h c}{e}) (\frac{1}{2 λ})$

$2.5 = \frac{12400}{2 λ}$

$λ = \frac{12400}{5} Å$

$λ = 2480 Å$

$λ = 2.48 \times 10^{- 7} m$

Q 16 :

Light is incident on a metallic plate having work function $110 \times 10^{- 20} J .$ If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s.
$(h = 6.63 \times 10^{- 34} J·s)$ [2026]

$1.66 \times 10^{15}$
$1.04 \times 10^{16}$
$1.04 \times 10^{13}$
$1.66 \times 10^{16}$

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(2)

$ϕ = h ν$

$ν = \frac{ϕ}{h}$

$ω = 2 π ν = \frac{2 π ϕ}{h} = \frac{2 \times 3.14 \times 110 \times 10^{- 2}}{6.63 \times 10^{- 34}}$

$ω = 1.04 \times 10^{16} rad/sec$

Q 17 :

A metal plate of area $2 \times 10^{- 4} m^{2}$ is illuminated by a radiation of intensity $8 m W / m^{2}$ . The work function of the metal is $5 e V$ . The energy of the incident photons is 10eV and only 1% of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be $[1 e V = 1.6 \times 10^{- 19} J]$

$10^{14}$ and $10 e V$
$10^{12}$ and $5 e V$
$10^{11}$ and $5 e V$
$10^{10}$ and $5 e V$

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(4)

$P = I A = 8 \times 10^{- 3} \times 2 \times 10^{- 4} = 16 \times 10^{- 7} W$

$Photons per sec = \frac{P}{h ν} = \frac{16 \times 10^{- 7}}{10 \times 1.6 \times 10^{- 19}} = 10^{12}$

$Photo electrons/sec = 10^{12} \times \frac{1}{100} = 10^{10}$

Q 18 :

For the photoelectric effect, the maximum kinetic energy $(E_{k})$ of the photoelectrons is plotted against the frequency (ν) of the incident photons as shown in figure. The slope of the graph gives

Ratio of Planck’s constant to electric charge
Work function of the metal
Charge of electron
Planck’s constant

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(4)

$K.E. = h f - ϕ$

$\tan θ = h$

Q 19 :

Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the photoelectrons emitted by the surface is $1.2 \times 10^{6}$ m/s. What is the wavelength of the light?

570 nm
710 nm
320 nm
194 nm

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(4)

$\frac{h c}{λ} = K E_{\max} = φ$

Q 20 :

The graphs show the variation of current $I$ (y-axis) in two photocells A & B as a function of the applied voltage V (x-axis) when light of same frequency is incident on the cell. Which of the following is the correct conclusion drawn from the data?

Cathodes of the two cells are made from the same substance, the intensity of light used are different
Cathodes are made from different substances and the intensity of light is the same
Cathode substances as well as intensity of light are different
No conclusion can be drawn

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(1)

Saturation current is different so intensity is different but stopping potential is same and frequency is same so cathode material also same.

Q 21 :

A certain metallic surface is illuminated by monochromatic radiation of wavelength $λ$ . The stopping potential for photoelectric current for this radiation is $3 V_{0}$ . If the same surface is illuminated with a radiation of wavelength $2 λ$ , the stopping potential is $V_{0}$ . The threshold wavelength of this surface for photoelectric effect is _____ $λ$ .

(4)

$K E = \frac{h c}{λ} - ϕ .....(i)$

$e (3 V_{0}) = \frac{h c}{λ_{0}} - ϕ .....(i)$

$e V_{0} = \frac{h c}{2 λ_{0}} - ϕ .....(ii)$

$Using (i) & (ii) ϕ = \frac{h c}{4 λ_{0}} = \frac{h c}{λ_{t}}$

$λ_{t} = 4 λ_{0}$

Q 22 :

A metallic surface is illuminated with radiation of wavelength $λ$ , the stopping potential is $V_{0}$ . If the same surface is illuminated with radiation of wavelength $2 λ$ , the stopping potential becomes $\frac{V_{0}}{4}$ . The threshold wavelength for this metallic surface will be-

$\frac{λ}{4}$
$4 λ$
$\frac{3}{2} λ$
$3 λ$

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(4)

$From the Einstein's photoelectric equation$

$e V_{0} = \frac{h c}{λ} - ϕ_{0} = \frac{h c}{λ} - \frac{h c}{λ_{0}}$ $. . . (i)$

$& \frac{e V_{0}}{4} = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$ $. . . (i i)$

$\Rightarrow \frac{1}{4} (\frac{h c}{λ} - \frac{h c}{λ_{0}}) = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$

$\Rightarrow \frac{1}{λ_{0}} - \frac{1}{4 λ_{0}} = \frac{1}{2 λ} - \frac{1}{4 λ}$

$\Rightarrow \frac{3}{4 λ_{0}} = \frac{1}{4 λ}$

$\Rightarrow λ_{0} = 3 λ$

Q 23 :

Assertion (A): Work function of aluminium is 4.2 eV. Emission of electron will not be possible if two photons each of energy 2.5 eV strike an electron of a aluminium

Reason (R): For photoelectron emission the energy of each photon should be greater than the work function of metal

Both A and R are true and R is the correct explanation of A
Both A and R are true and R is not the correct explanation of A
A is true and R is false
A is false and R is true

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(1)

Conceptual

Q 24 :

For a certain metal, when monochromatic light of wavelength $λ$ is incident, the stopping potential for photoelectrons is $3 V_{0}$ . When the same metal is illuminated by light of wavelength $2 λ$ , then the stopping potential becomes $V_{0}$ . The threshold wavelength for photoelectric emission for the given metal is $α λ$ . The value of $α$ is _____. [2026]

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4
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3

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(2)

$\frac{h c}{λ} - ϕ = 3 e V_{0}$ $. . . (i)$

$\frac{h c}{2 λ} - ϕ = e V_{0}$ $. . . (i i)$

$From (i) and (ii): \frac{h c}{λ} - ϕ = 3 [\frac{h c}{2 λ} - ϕ]$

$\Rightarrow ϕ = \frac{h c}{4 λ}$

$\frac{h c}{λ_{0}} = \frac{h c}{4 λ} \Rightarrow λ_{0} = 4 λ$

$\Rightarrow α = 4$

Q 25 :

The graph shows variation of stopping potential $V_{0}$ with the frequency $ν$ of the incident radiation for three photosensitive metals $X_{1}$ , $X_{2}$ and $X_{3}$ . Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [2026]

$X_{1}$
$X_{2}$
$X_{3}$
All the metals will give out photo electrons with same kinetic energies.

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(1)

$V_{0} = \frac{E}{e} - \frac{ϕ}{e}$

$K E_{\max} = E - h ν_{th}$

$K E_{\max} is highest for least ν_{th}$

$As metal (1) having minimum value of work function$

$So X_{1} will have maximum kinetic energy$

Q 26 :

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $α \times 10^{- 19} J$ . The value of $α$ is _______. [2026]

( $h = 6.62 \times 10^{- 34} Js, e = 1.6 \times 10^{- 19} C$ and $c = 3 \times 10^{8} m/s$ )

3.68
4.68
5.68
2.68

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(3)

$λ = 331 nm$

$V_{s} = 0.2 V$

$e V_{s} = \frac{h c}{λ} - ϕ$

$ϕ = \frac{1240}{331} eV - 0.2 eV = 3.546 eV$

$\Rightarrow ϕ = 3.546 \times 1.6 \times 10^{- 19} J = 5.67 \times 10^{- 19} J$

Q 27 :

$K_{1}$ and $K_{2}$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $λ_{1}$ and $λ_{2}$ , respectively. If $λ_{1} = 2 λ_{2}$ , then the work function of material is given by [2026]

$K_{2} + 2 K_{1}$
$2 K_{2} - K_{1}$
$K_{1} - 2 K_{2}$
$K_{2} - 2 K_{1}$

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(4)

$K_{1} = \frac{h c}{λ_{1}} - ϕ and K_{2} = \frac{h c}{λ_{2}} - ϕ$

$K_{2} = \frac{h c}{\frac{λ_{1}}{2}} - ϕ = 2 (\frac{h c}{λ_{1}}) - ϕ$

$K_{2} = 2 (K_{1} + ϕ) - ϕ = 2 K_{1} + ϕ$

$ϕ = K_{2} - 2 K_{1}$

Topic Question Set

Q 12 :

The difference between threshold wavelengths for two metal surfaces A and B having work function $ϕ_{A} = 9 eV$ and $ϕ_{B} = 4.5 eV$ in nm is: (Given, $h c = 1242 eV nm$ ) [2023]

Q 16 :

Light is incident on a metallic plate having work function $110 \times 10^{- 20} J .$ If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s.
$(h = 6.63 \times 10^{- 34} J·s)$ [2026]

Q 18 :

For the photoelectric effect, the maximum kinetic energy $(E_{k})$ of the photoelectrons is plotted against the frequency (ν) of the incident photons as shown in figure. The slope of the graph gives

Q 19 :

Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the photoelectrons emitted by the surface is $1.2 \times 10^{6}$ m/s. What is the wavelength of the light?

Q 20 :

The graphs show the variation of current $I$ (y-axis) in two photocells A & B as a function of the applied voltage V (x-axis) when light of same frequency is incident on the cell. Which of the following is the correct conclusion drawn from the data?

Q 22 :

A metallic surface is illuminated with radiation of wavelength $λ$ , the stopping potential is $V_{0}$ . If the same surface is illuminated with radiation of wavelength $2 λ$ , the stopping potential becomes $\frac{V_{0}}{4}$ . The threshold wavelength for this metallic surface will be-

Q 23 :

Assertion (A): Work function of aluminium is 4.2 eV. Emission of electron will not be possible if two photons each of energy 2.5 eV strike an electron of a aluminium

Reason (R): For photoelectron emission the energy of each photon should be greater than the work function of metal

Q 25 :

The graph shows variation of stopping potential $V_{0}$ with the frequency $ν$ of the incident radiation for three photosensitive metals $X_{1}$ , $X_{2}$ and $X_{3}$ . Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [2026]

Q 27 :

$K_{1}$ and $K_{2}$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $λ_{1}$ and $λ_{2}$ , respectively. If $λ_{1} = 2 λ_{2}$ , then the work function of material is given by [2026]

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Topic Question Set

Q 11 : A metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V0. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential becomes V04. The threshold wavelength for this metallic surface will be [2023]

Q 12 : The difference between threshold wavelengths for two metal surfaces A and B having work function ϕA=9 eV and ϕB=4.5 eV in nm is: (Given, hc=1242 eV nm) [2023]

Q 14 : A light wave described by E=60[sin(3×1015)t+sin(12×1015)t] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately) ______ eV. (h=6.6×10-34 J·s and e=1.6×10-19 C) [2026]

Q 16 : Light is incident on a metallic plate having work function 110×10-20J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s. (h=6.63×10-34 J·s) [2026]

Q 18 : For the photoelectric effect, the maximum kinetic energy (Ek) of the photoelectrons is plotted against the frequency (ν) of the incident photons as shown in figure. The slope of the graph gives

Q 19 : Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the photoelectrons emitted by the surface is 1.2×106 m/s. What is the wavelength of the light?

Q 20 : The graphs show the variation of current I (y-axis) in two photocells A & B as a function of the applied voltage V (x-axis) when light of same frequency is incident on the cell. Which of the following is the correct conclusion drawn from the data?

Q 22 : A metallic surface is illuminated with radiation of wavelength λ, the stopping potential is V0. If the same surface is illuminated with radiation of wavelength 2λ, the stopping potential becomes V04. The threshold wavelength for this metallic surface will be-

Q 23 : Assertion (A): Work function of aluminium is 4.2 eV. Emission of electron will not be possible if two photons each of energy 2.5 eV strike an electron of a aluminium Reason (R): For photoelectron emission the energy of each photon should be greater than the work function of metal

Q 25 : The graph shows variation of stopping potential V0 with the frequency ν of the incident radiation for three photosensitive metals X1, X2 and X3. Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [2026]

Q 26 : Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is α×10-19J. The value of α is _______. [2026] (h=6.62×10-34Js, e=1.6×10-19C and c=3×108m/s)

Q 27 : K1 and K2 be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength λ1 and λ2, respectively. If λ1=2λ2, then the work function of material is given by [2026]

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Q 12 :

The difference between threshold wavelengths for two metal surfaces A and B having work function $ϕ_{A} = 9 eV$ and $ϕ_{B} = 4.5 eV$ in nm is: (Given, $h c = 1242 eV nm$ ) [2023]

Q 16 :

Light is incident on a metallic plate having work function $110 \times 10^{- 20} J .$ If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ rad/s.
$(h = 6.63 \times 10^{- 34} J·s)$ [2026]

Q 18 :

For the photoelectric effect, the maximum kinetic energy $(E_{k})$ of the photoelectrons is plotted against the frequency (ν) of the incident photons as shown in figure. The slope of the graph gives

Q 19 :

Light is incident on the surface of metallic sodium, whose work function is 2.3 eV. The maximum speed of the photoelectrons emitted by the surface is $1.2 \times 10^{6}$ m/s. What is the wavelength of the light?

Q 20 :

The graphs show the variation of current $I$ (y-axis) in two photocells A & B as a function of the applied voltage V (x-axis) when light of same frequency is incident on the cell. Which of the following is the correct conclusion drawn from the data?

Q 22 :

A metallic surface is illuminated with radiation of wavelength $λ$ , the stopping potential is $V_{0}$ . If the same surface is illuminated with radiation of wavelength $2 λ$ , the stopping potential becomes $\frac{V_{0}}{4}$ . The threshold wavelength for this metallic surface will be-

Q 23 :

Assertion (A): Work function of aluminium is 4.2 eV. Emission of electron will not be possible if two photons each of energy 2.5 eV strike an electron of a aluminium

Reason (R): For photoelectron emission the energy of each photon should be greater than the work function of metal

Q 25 :

The graph shows variation of stopping potential $V_{0}$ with the frequency $ν$ of the incident radiation for three photosensitive metals $X_{1}$ , $X_{2}$ and $X_{3}$ . Which metal will give out electrons with greater kinetic energy, for the same wavelength of incident radiation? [2026]

Q 27 :

$K_{1}$ and $K_{2}$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $λ_{1}$ and $λ_{2}$ , respectively. If $λ_{1} = 2 λ_{2}$ , then the work function of material is given by [2026]