NEET Physics PYQ – Dual Nature of Radiation and Matter Important Questions

Q 1 :
If $ϕ$ is the work function of photosensitive material in eV and light of wavelength of numerical value $λ = \frac{h c}{e} metre,$ is incident on it with energy above its threshold value at an instant, then the maximum kinetic energy of the photo-electron ejected by it at that instant (Take $h$ - Planck’s constant, $c$ - velocity of light in free space) is (in SI units) [2024]

$e + 2 ϕ$
$2 e - ϕ$
$e - ϕ$
$e + ϕ$

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(3)

According to Einstein photoelectric equation,

$Photon energy = K.E. + Work function$

Here, photon energy $= e$ $e V$

Work function $= ϕ$ $e V$

$∴$ $e = K.E. + ϕ \Rightarrow K.E. = e - ϕ$

Q 2 :
The maximum kinetic energy of the emitted photoelectrons in photoelectric effect is independent of: [2023]

work function of material
intensity of incident radiation
frequency of incident radiation
wavelength of incident radiation

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(2)

Using photoelectric equation,

$E = h υ - ϕ_{0}$

Maximum kinetic energy of emitted electron is independent of intensity of radiation.

The intensity of incident radiation varies with photo current if threshold frequency requirement is fulfilled.

Q 3 :
When two monochromatic light of frequency, $υ$ and $\frac{υ}{2}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_{s}}{2}$ and $V_{s}$ respectively. The threshold frequency for this metal is [2022]

$2 υ$
$3 υ$
$\frac{2}{3} υ$
$\frac{3}{2} υ$

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(4)

Let the threshold frequency be $υ_{0}$ .

By using the equation of photoelectric effect, $E = h υ_{0} + e V_{0}$

Case I : $h υ = h υ_{0} + \frac{e V_{s}}{2}$ ...(i)

Case II: $\frac{h υ}{2} = h υ_{0} + e V_{s}$ ...(ii)

$\frac{h υ}{2} = \frac{- e V_{s}}{2}$

$- h υ = e V_{s} (put in (i))$

$h υ = h υ_{0} - \frac{h υ}{2} \Rightarrow υ_{0} = \frac{3}{2} υ$

Q 4 :
The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photon emission from the substance is (approximately) [2019]

3100 nm
966 nm
31 nm
310 nm

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(4)

Required wavelength of light,

$λ_{0} = \frac{h c}{ϕ} = \frac{1240 eV nm}{4 eV} \approx 310 nm$

Q 5 :
When the light of frequency $2 υ_{0}$ (where $υ_{0}$ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is $v_{1}$ . When the frequency of the incident radiation is increased to $5 υ_{0}$ , the maximum velocity of electrons emitted from the same plate is $v_{2}$ . The ratio of $v_{1}$ to $v_{2}$ is [2018]

1 : 2
1 : 4
4 : 1
2 : 1

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(1)

According to the Einstein’s photoelectric equation,

$E = W_{0} + \frac{1}{2} m v^{2}$

When frequency of incident light is $2 υ_{0}$ .

$h (2 υ_{0}) = h υ_{0} + \frac{1}{2} m v_{1}^{2} \Rightarrow h υ_{0} = \frac{1}{2} m v_{1}^{2}$ ...(i)

When frequency of incident light is $5 υ_{0}$

$h (5 υ_{0}) = h υ_{0} + \frac{1}{2} m v_{2}^{2} \Rightarrow 4 h υ_{0} = \frac{1}{2} m v_{2}^{2}$ ...(ii)

Dividing (i) by (ii), $\frac{1}{4} = \frac{v_{1}^{2}}{v_{2}^{2}} or \frac{v_{1}}{v_{2}} = \frac{1}{2}$

Q 6 :
Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is [2016]

+3 V
+4 V
–1 V
–3 V

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(4)

According to Einstein's photoelectric equation, maximum kinetic energy of photoelectrons,

$K E_{max} = E_{ν} - ϕ$

or $2 = 5 - ϕ ∴ ϕ = 3 eV$

When $E_{ν} = 6$ eV then, $K E_{max} = 6 - 3 = 3$ eV

or $e (V_{cathode} - V_{anode}) = 3$ eV

or $V_{cathode} - V_{anode} = 3 V = - V_{stopping}$

$∴$ $V_{stopping} = - 3$ V

Q 7 :
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 $2 λ$ , the stopping potential is $\frac{V}{4}$ . The threshold wavelength for the metallic surface is [2016]

$\frac{5}{2} λ$
$3 λ$
$4 λ$
$5 λ$

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(2)

According to Einstein's photoelectric equation,

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

$∴$ $As per question, e V = \frac{h c}{λ} - \frac{h c}{λ_{0}}$ ...(i)

$\frac{e V}{4} = \frac{h c}{2 λ} - \frac{h c}{λ_{0}}$ ...(ii)

From equations (i) and (ii), we get

$\frac{h c}{2 λ} - \frac{h c}{4 λ} = \frac{h c}{λ_{0}} - \frac{h c}{4 λ_{0}} \Rightarrow \frac{h c}{4 λ} = \frac{3 h c}{4 λ_{0}}$ or $λ_{0} = 3 λ$

Q 8 :
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 surface of the material is ( $h$ = Planck’s constant, $c$ = speed of light) [2015]

$\frac{2 h c}{λ}$
$\frac{h c}{3 λ}$
$\frac{h c}{2 λ}$
$\frac{h c}{λ}$

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(3)

Let $ϕ_{0}$ be the work function of the surface of the material.
According to Einstein’s photoelectric equation, the maximum kinetic energy of the emitted photoelectrons in the first case is

$K_{{max}_{1}} = \frac{h c}{λ} - ϕ_{0}$

and that in the second case is

$K_{{max}_{2}} = \frac{h c}{\frac{λ}{2}} - ϕ_{0} = \frac{2 h c}{λ} - ϕ_{0}$

But $K_{{max}_{2}} = 3 K_{{max}_{1}}$ (given)

$∴$ $\frac{2 h c}{λ} - ϕ_{0} = 3 (\frac{h c}{λ} - ϕ_{0});$ $\frac{2 h c}{λ} - ϕ_{0} = \frac{3 h c}{λ} - 3 ϕ_{0}$

$3 ϕ_{0} - ϕ_{0} = \frac{3 h c}{λ} - \frac{2 h c}{λ} or 2 ϕ_{0} = \frac{h c}{λ} or ϕ_{0} = \frac{h c}{2 λ}$

Q 9 :
A certain metallic surface is illuminated with monochromatic light of wavelength, $λ$ . The stopping potential for photoelectric current for this light is $3 V_{0}$ . If the same surface is illuminated with light of wavelength $2 λ$ , the stopping potential is $V_{0}$ . The threshold wavelength for this surface for photoelectric effect is [2015]

$\frac{λ}{4}$
$\frac{λ}{6}$
$6 λ$
$4 λ$

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(4)

Q 10 :
When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increased from 0.5 eV to 0.8 eV. The work function of the metal is [2014]

0.65 eV
1.0 eV
1.3 eV
1.5 eV

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(2)

According to Einstein's photoelectric equation, the kinetic energy of emitted photoelectrons is

$K = h υ - ϕ_{0}$

where $h υ$ is the energy of incident radiation and $ϕ_{0}$ is the work function of the metal.

As per question,

$0.5 eV = h υ - ϕ_{0}$ ...(i)

$0.8 eV = 1.2 h υ - ϕ_{0}$ ...(ii)

On solving eqns. (i) and (ii), we get

$ϕ_{0} = 1.0$ $eV$

Topic Question Set

Q 2 :
The maximum kinetic energy of the emitted photoelectrons in photoelectric effect is independent of: [2023]

Q 3 :
When two monochromatic light of frequency, $υ$ and $\frac{υ}{2}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_{s}}{2}$ and $V_{s}$ respectively. The threshold frequency for this metal is [2022]

Q 4 :
The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photon emission from the substance is (approximately) [2019]

Q 6 :
Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is [2016]

Q 7 :
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 $2 λ$ , the stopping potential is $\frac{V}{4}$ . The threshold wavelength for the metallic surface is [2016]

(4)

Q 10 :
When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increased from 0.5 eV to 0.8 eV. The work function of the metal is [2014]

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Topic Question Set

Q 2 : The maximum kinetic energy of the emitted photoelectrons in photoelectric effect is independent of: [2023]

Q 3 : When two monochromatic light of frequency, υ and υ2 are incident on a photoelectric metal, their stopping potential becomes Vs2 and Vs respectively. The threshold frequency for this metal is [2022]

Q 4 : The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photon emission from the substance is (approximately) [2019]

Q 6 : Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is [2016]

Q 7 : 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 V4. The threshold wavelength for the metallic surface is [2016]

(4)

Q 10 : When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increased from 0.5 eV to 0.8 eV. The work function of the metal is [2014]

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Q 2 :
The maximum kinetic energy of the emitted photoelectrons in photoelectric effect is independent of: [2023]

Q 3 :
When two monochromatic light of frequency, $υ$ and $\frac{υ}{2}$ are incident on a photoelectric metal, their stopping potential becomes $\frac{V_{s}}{2}$ and $V_{s}$ respectively. The threshold frequency for this metal is [2022]

Q 4 :
The work function of a photosensitive material is 4.0 eV. The longest wavelength of light that can cause photon emission from the substance is (approximately) [2019]

Q 6 :
Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is [2016]

Q 7 :
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 $2 λ$ , the stopping potential is $\frac{V}{4}$ . The threshold wavelength for the metallic surface is [2016]

Q 10 :
When the energy of the incident radiation is increased by 20%, the kinetic energy of the photoelectrons emitted from a metal surface increased from 0.5 eV to 0.8 eV. The work function of the metal is [2014]