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The value of Plank's constant, if the slope of the graph of stopping potential vs frequency of incident light is $4 \times 10^{- 15} V s$ is (given charge of an electron $= 1.6 \times 10^{- 19} C$ )

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Important Questions on Dual Nature of Radiation and Matter

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Following graphs show the variation of stopping potential corresponding to the frequency of incident radiation

(f)

for a given metal. The correct variation is shown in graph (

f_{0} =

Threshold frequency)

Question Image

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

A pulse of light of duration

100 ns

is absorbed completely by a small object initially at rest. Power of the pulse is

30 mW

and the speed of light is

3 \times 10^{8} m s^{- 1}

. The final momentum of the object is

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio

u_{1} : u_{2} = 2 : 1

and

h c = 1240 eV nm

, the work function of the metal is nearly

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Light of wavelength

500 nm

is incident on a metal with work function

2.28 eV.

The de Broglie wavelength of the emitted electron is:

HARD

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Electrons are emitted with kinetic energy $T$ from a metal plate by an irradiation of light of intensity $J$ and frequency $v .$ Then, which of the following will be true?

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

A photoelectric material having work-function

ϕ_{0}

is illuminated with a light of wavelength

λ (λ < \frac{h c}{ϕ_{0}})

. The fastest photoelectron has a de Broglie wavelength

λ_{d}

. A change in wavelength of the incident light by

Δ λ

results in a change

Δ λ_{d}

λ_{d}

. The ratio

\frac{Δ λ_{d}}{Δ λ}

is proportional to

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Radiation of wavelength

λ

is incident on a photocell. The fastest emitted photoelectron has a speed

v

. If the wavelength is changed to

\frac{3 λ}{4}

, the speed of the fastest emitted photoelectron will be

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

In an experimental observation of the photoelectric effect, the stopping potential was plotted against the incident light frequency as shown in the figure below:

Question Image

If the work function of the metal is given by $ϕ_{0}$ , the angle $α$ is given by

(Here, $h$ and $e$ are Planck's constant and charge of electron respectively).

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

A photoelectric surface is illuminated successively by monochromatic light of wavelength

λ

and

\frac{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)

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

When a certain metallic surface is illuminated with monochromatic light of wavelength

λ,

the stopping potential for photoelectric current is

3 V_{0}

and when the same surface is illuminated with light of wavelength

2 λ,

the stopping potential is

V_{0} .

The threshold wavelength of this surface for photoelectric effect is

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

In a photoelectric effect measurement, the stopping potential for a given metal is found to be

V_{0}

volt

when radiation of wavelength

λ_{0}

is used. If radiation of wavelength

{2 λ}_{0}

is used with the same metal then the stopping potential (in

volt

) will be

HARD

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength

(λ)

of incident light and the corresponding stopping potential

(V_{0})

are given below:

$λ (μ m)$	$V_{0} (v o l t)$
0.3	2.0
0.4	1.0
0.5	0.4

Given that

c = 3 \times 10^{8} m s^{- 1} and e = 1.6 \times 10^{- 19} C,

Planck's constant (in units of

J s

) found from such an experiment is :

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

In a photoelectric effect experiment, the graph of stopping potential $V$ versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased :

Question Image

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

A photoelectric surface is illuminated successively by monochromatic light of wavelengths

λ and \frac{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 is :

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

The graph between maximum kinetic energy and intensity of light in photoelectric effect is plotted. Out of the four graphs $A, B, C, D$ shown in the figure, the correct graph is

Question Image

EASY

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

According to Einstein's photoelectric equation, the graph between kinetic energy of photoelectrons ejected and the frequency of incident radiation is

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

The radiation corresponding to

3 \to 2

transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of

5 \times 10^{- 4} T

. Assume that the radius of the largest circular path followed by these electrons is

7 mm

, the work function of the metal is:
(Mass of electron

= 9.1 \times 10^{- 31} kg

)

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Photons with energy of

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

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

Light of wavelength

500 nm

is incident on a metal with work function

2.28 eV

. The de Broglie wavelength of the emitted electron is:

MEDIUM

Physics>Modern Physics>Dual Nature of Radiation and Matter>Einstein's Equation of Photoelectric Effect

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:

The value of Plank's constant, if the slope of the graph of stopping potential vs frequency of incident light is 4×10-15 V s is (given charge of an electron =1.6×10-19 C)

Important Questions on Dual Nature of Radiation and Matter

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The value of Plank's constant, if the slope of the graph of stopping potential vs frequency of incident light is $4 \times 10^{- 15} V s$ is (given charge of an electron $= 1.6 \times 10^{- 19} C$ )