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Photons of wavelength $248 nm$ fall on a metal surface whose work function is $2.2 eV$ . Assume that each photoelectron inside the metal lattice may come out of the surface orcollide with the lattice before coming out. In each collision with the lattice, it loses $20 %$ of its existing energy. Which of the following can be a kinetic energy of an ejected photoelectron?

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Important Questions on Dual Nature of Matter and Radiation

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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).

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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 Matter and Radiation>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 Matter and Radiation>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>Dual Nature of Matter and Radiation>Photoelectric Effect

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}

EASY

Physics>Modern Physics>Dual Nature of Matter and Radiation>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>Dual Nature of Matter and Radiation>Photoelectric Effect

The radiation corresponding to

3 \to 2

transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of

3 \times 1 0^{- 4} T

. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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

HARD

Physics>Modern Physics>Dual Nature of Matter and Radiation>Photoelectric Effect

Light of wavelength $λ_{p h}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $ϕ$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $λ_{e},$ which of the following statement(s) is(are) true ?
Question Image

HARD

Physics>Modern Physics>Dual Nature of Matter and Radiation>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]

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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>Dual Nature of Matter and Radiation>Photoelectric Effect

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

)

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>Photoelectric Effect

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

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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>Dual Nature of Matter and Radiation>Photoelectric Effect

For photo-electric effect with incident photon wavelength

λ

, the stopping potential is

V_{0}

. Identify the correct variation(s) of

V_{0}

with

λ

and

\frac{1}{λ}

MEDIUM

Physics>Modern Physics>Dual Nature of Matter and Radiation>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

HARD

Physics>Modern Physics>Dual Nature of Matter and Radiation>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)

HARD

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

Important Questions on Dual Nature of Matter and Radiation

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