A metal has a work function of 2.0 e V and is illuminated by monochromatic light of wavelength 500 n m . Calculate ( h = 6 .6 × 10 - 34 Js , c = 3 × 10 8 m / s ) The threshold wavelength The maximum energy of photoelectrons The stopping potential

(i) Given, Work function, W 0 = 2.0 e V = 2 .0 × 1 .6 × 10 - 19 J Wavelength of monochromatic light is , λ = 500 n m Say, the threshold wavelength is λ 0 . Expression for work function, W 0 = h c λ 0 ∴ λ 0 = h c W 0 = 6.6 × 10 - 34 × 3 × 10 8 2.0 × 1.6 × 10 - 19 m ∴ λ 0 = 6.1875 × 10 - 7 m = 6187.5 Å (ii) According to Einstein’s photoelectron equation, the maximum kinetic energy is given by, K m a x = h c λ - W 0 K m a x = 6.6 × 10 - 34 × 3 × 10 8 500 × 10 - 9 × 1.6 × 10 - 19 - 2.0 e V K m a x = 2.475 - 2.0 = 0.475 e V (iii) Stopping potential, V 0 = K m a x e = 0.475 V

What is the de Broglie wavelength associated with (Take, the mass of the electron as, m = 9 . 1 × 10 - 31 kg , h = 6 . 6 × 10 - 34 Js ) (i) an electron moving with a speed of 5 . 4 × 10 6 ms - 1 and (ii) a ball of mass 1 . 50 g travelling at 30 . 0 m / s ?

(i) Given, The speed of the electron, v = 5 . 4 × 10 6 m / s The mass of the electron, m = 9 . 1 × 10 - 31 kg The Plank's constant, h = 6 . 6 × 10 - 34 Js We know that de Broglie wavelength is given as, λ = h P = h m v = 6 · 6 × 10 - 34 9 . 1 × 10 - 31 × 5 . 4 × 10 6 m = 0 . 135 × 10 - 9 m = 0 . 135 nm (ii) Given, the mass of the ball, m = 1 . 5 g = 1 . 5 × 10 - 3 kg The speed of the ball, v = 30 m/s Like in the case of an electron, the de Broglie wavelength of the ball becomes, λ = h m v = 6 . 6 × 10 - 34 1 . 5 × 10 - 3 × 30 = 1 . 47 × 10 - 32 m

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The work function, for a given photosensitive surface equals $2.5 e V$ . When light of frequency, $ν$ , falls on this surface, the emitted photoelectrons are completley stopped by applying a retarding potential of $4.1 V$ . What is the value of $ν$ ?

Important Questions on Dual Nature of Radiation and Matter

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 24

When light of frequency

2.4 \times 10^{15} H z

, falls on a photosensitive surface, the retarding potential needed to completely stop the emitted photoelectrons is found to be

6.8 V

. What is the work function in

e V

of the given photosensitive surface?

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 25

Ultraviolet radiations of wavelength

800 Å

and

700 Å

, when allowed to fall on a photosensitive surface are found to liberate electrons with maximum kinetic energies of

2 e V

and

4.1 e V

respectively. Calculate the value of Planck's constant.

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 26

Find the frequency of light which ejects electrons from a metal surface, fully stopped by a retarding potential of

3.3 V

. If photoelectric emission begins in this metal at a frequency of

8 \times 10^{14} H z

, calculate the work function

(e V)

for this metal. Take

h = 6 .63 \times 10^{- 34} Js

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 27

When

U V

light of wavelength

300 n m

is incident on a metal plate, a negative potential of

0.59 V

is required to stop the emission of photoelectrons. Calculate the energy of the incident photon and the work function for the metal in

e V

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 28

A metal has a work function of

2.0 e V

and is illuminated by monochromatic light of wavelength

500 n m

. Calculate (

h = 6 .6 \times 10^{- 34} Js, c = 3 \times 10^{8} m / s

)

The threshold wavelength
The maximum energy of photoelectrons
The stopping potential

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 1

What is the de Broglie wavelength associated with (Take, the mass of the electron as, $m = 9.1 \times 10^{- 31} kg, h = 6.6 \times 10^{- 34} Js$ )
(i) an electron moving with a speed of $5.4 \times 10^{6} {ms}^{- 1}$ and
(ii) a ball of mass $1.50 g$ travelling at $30.0 m / s ?$

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 2

An electron is accelerated through a potential difference of

64 V

. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond. Mass of the electron,

m = 9.1 \times 10^{- 31} kg

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12th CBSE

IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 3 - Dual Nature of Radiation and Matter>Problems For Practice>Q 3

What potential difference must be applied to an electron microscope to produce an electron beam of wavelength

0.41 A^{0}

The work function, for a given photosensitive surface equals 2.5 eV. When light of frequency, ν, falls on this surface, the emitted photoelectrons are comp­letley stopped by applying a retarding potential of 4.1 V. What is the value of ν?

Important Questions on Dual Nature of Radiation and Matter

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The work function, for a given photosensitive surface equals $2.5 e V$ . When light of frequency, $ν$ , falls on this surface, the emitted photoelectrons are completley stopped by applying a retarding potential of $4.1 V$ . What is the value of $ν$ ?