HARD

Earn 100

A light source emits radiations of $λ = 310 nm$ . Number of photons emitted per second by this source varies with time, as $N = 10^{18} t^{2}$ . ( $t$ in sec). If this light source is used to emit photoelectrons from a metal of work function $3.1 eV$ . Find the time during which the total maximum possible kinetic energy of all the emitted photoelectrons from the beginning is $1296 J$ .
$(Use E (eV) = \frac{12400}{λ (Å)})$

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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

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>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

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

HARD

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

In a photoelectric experiment, a parallel beam of monochromatic light with the power of

200 W

is incident on a perfectly absorbing cathode of work function

6.25 eV

. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of

500 V

is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force

F = n \times 10^{- 4} N

due to the impact of the electrons. The value of

n

is __________. Mass of the electron

m_{e} = 9 \times 10^{- 31} kg a n d 1.0 eV = 1.6 \times 10^{- 19} J

MEDIUM

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

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 :

MEDIUM

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

The continuous part of

X

-ray spectrum is a result of the

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:

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]

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

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>Dual Nature of Matter and Radiation>Photoelectric Effect

When a certain photosensitive surface is illuminated with a monochromatic light of frequency

ν,

the stopping potential of the photo current is

- \frac{V_{0}}{2} .

When the surface is illuminated by monochromatic light of frequency

\frac{ν}{2},

the stopping potential is

- V_{0} .

The threshold frequency for photoelectric emission is

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

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:

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

]

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

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)

EASY

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

Maximum kinetic energy of a photoelectric varies with the frequency

(f)

of the incident radiation as

EASY

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

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)

Important Questions on Dual Nature of Matter and Radiation

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