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The anode voltage of a photocell is kept fixed. The wavelength $λ$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows

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Important Questions on Dual Nature of Matter and Radiation

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

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 Matter and Radiation>Einstein's Photoelectric Equation

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

EASY

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

Maximum kinetic energy of a photoelectric varies with the frequency

(f)

of the incident radiation as

MEDIUM

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

When the light of frequency

2 ν_{0}

(where

ν_{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 ν_{0},

the maximum velocity of electrons emitted from the same plate is

v_{2} .

The ratio of

v_{1} t o v_{2}

HARD

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

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 :

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

Photons of wavelength

λ

are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular are of radius R by a perpendicular magnetic field having a magnitude B. The work function of the metal is (Where symbols have their usual meanings).

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

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:

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

A laser light of wavelength

660 nm

is used to weld Retina detachment. If a laser pulse of width

60 ms

and power

0.5 kW

is used, the approximate number of photons in the pulse are (Take Planck's Constant,

h = 6.62 \times 10^{- 34} J s)

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

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 Matter and Radiation>Einstein's Photoelectric Equation

A metal plate of area

1 \times 10^{- 4} m^{2}

is illuminated by a radiation of intensity

16 mW m^{- 2}

. The work function of the metal is

5 eV .

The energy of the incident photons is

10 eV

and only

10 %

of it produces photo electrons. The number of emitted photo electron per second and their maximum energy, respectively, will be:

[1 eV = 1.6 \times 10^{- 19} J]

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

On a photosensitive material, when the frequency of incident radiation is increased by

30 %

, the kinetic energy of emitted photoelectrons increases from

0.4 eV

0.9 eV

. The work function of the surface is

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

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 Matter and Radiation>Einstein's Photoelectric Equation

The electric field of certain radiation is given by the equation

E = 200 \{\sin (4 π \times 10^{10}) t + \sin (4 π \times 10^{15}) t\}

falls in a metal surface having work function

2 .0 eV .

The maximum kinetic energy

(in eV)

of the photoelectrons is [Planck's constant

(h) = 6.63 \times 10^{- 34} J s

and electron charge

e = 1.6 \times 10^{- 19} C

]

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

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

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

The maximum velocity of the photoelectrons emitted from the surface is

v

when light of frequency

n

falls on a metal surface. If the incident frequency is increased to

3 n

, the maximum velocity of the ejected photoelectrons will be:

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

Photons of energy

7 eV

are incident on two metals

A

and

B

with work functions

6 eV

and

3 eV

, respectively. The minimum de-Broglie wavelengths of the emitted photoelectrons with maximum energies are

λ_{A}

and

λ_{B}

, respectively, where

\frac{λ_{A}}{λ_{B}}

is nearly,

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

In a photocell circuit, the stopping potential, $V_{0}$ is a measure of the maximum kinetic energy of the photoelectrons. The following graph shows experimentally measured values of stopping potential versus frequency, $(ν)$ of incident light.

Question Image

The values of Planck's constant and the work function as determined from the graph are (taking the magnitude of electronic charge to be, $e = 1.6 \times 10^{- 19} C$ ),

HARD

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

The magnetic field associated with a light wave is given, at the origin, by

B = B_{0} [\sin (3.14 \times 10^{7}) c t + \sin (6.28 \times 10^{7}) c t] .

If this light falls on a silver plate having a work function of

4 .7 eV,

what will be the maximum kinetic energy of the photoelectrons?

(c = 3 \times 10^{8} m s^{- 1}, h = 6 .6 \times 10^{- 34} J s)

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

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:

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

The surface of certain metal is first illuminated with light of wavelength

λ_{1} = 350 n m

and then, by a light of wavelength

λ_{2} = 540 n m .

It is found that the maximum speed of the photoelectrons in the two cases differ by a factor of

2

. The work function of the metal (in

e V

) is close to
(Energy of photon

= \frac{1240}{λ (i n n m)} e V

)

The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows

Important Questions on Dual Nature of Matter and Radiation

Learn and Prepare for any exam you want !

The anode voltage of a photocell is kept fixed. The wavelength $λ$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows