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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.

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

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Important Questions on Modern Physics

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Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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:

MEDIUM

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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:

EASY

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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

]

HARD

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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>Modern Physics>Dual Nature of Light and Matter: 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>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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,

HARD

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

When photons of wavelength

λ_{1}

are incident on an isolated sphere, the corresponding stopping potential is found to be

V

. When photons of wavelength

λ_{2}

are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength

λ_{3}

is used then find the stopping potential for this case:

MEDIUM

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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).

EASY

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

The photoelectric threshold wavelength of silver is

3250 \times 10^{- 10} m

. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength

2536 \times 10^{- 10} m

is:-

(G i v e n h = 4.14 \times 10^{- 15} eV s a n d c = 3 \times 10^{8} m s^{- 1})

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Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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:

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Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

When ultraviolet radiation of a certain frequency falls on a potassium target, the photoelectrons released can be stopped completely by a retarding potential of

0.6 V .

If the frequency of the radiation is increased by

10 %,

this stopping potential rises to

0.9 V .

The work function of potassium is

MEDIUM

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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)

MEDIUM

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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

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Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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>Modern Physics>Dual Nature of Light and Matter: 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 :

MEDIUM

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

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

EASY

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: Photoelectric Effect

Maximum kinetic energy of a photoelectric varies with the frequency

(f)

of the incident radiation as

HARD

Physics>Modern Physics>Modern Physics>Dual Nature of Light and Matter: 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 :

Important Questions on Modern Physics

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