The threshold frequency for a certain metal is 3 . 3 × 10 14 Hz . If light of frequency 8 . 2 × 10 14 Hz is incident on the metal, predict the cutoff voltage for the photoelectric emission.

Given: The threshold frequency of the metal is, ν 0 = 3.3 × 1 0 14 Hz The frequency of incident light on metal is, ν = 8.2 × 1 0 14 Hz Also, the charge of an electron is, e = 1.6 × 1 0 - 19 C The plank’s constant is, h = 6.626 × 1 0 - 34 Js The cut-off energy is, e V 0 = h ( ν - ν 0 ) So, V 0 = h ( ν − ν 0 ) e = 6 .626 × 10 − 34 × 8 .2 × 10 14 − 3 .3 × 10 14 1 .6 × 10 − 19 = 2 .03 V Thus, the cut-off voltage for the photoelectric emission is 2 .03 V .

What is the (a) momentum, (b) speed, and (c) de Broglie wavelength of an electron with kinetic energy of 120 eV .

Kinetic energy of electron, E K = 120 eV = 120 × 1 . 6 × 10 - 19 J Mass of electron = 9 . 1 × 10 - 31 Kg (a) We know that, Kinetic energy is given as, E K = 1 2 m v 2 ∴ v = 2 E K m = 2 × 120 × 1 . 6 × 10 - 19 9 . 1 × 10 - 31 = 6 . 496 × 10 6 m / s Now, by using the formula, P = m v , P = 9 . 1 × 10 - 31 × 6 . 496 × 10 6 = 5 . 91 × 10 - 24 Kgm / s ∴ Momentum of electron is 5 . 91 × 10 - 24 Kgm / s . (b) Speed of electron is already calculated in part (a), v = 6 . 496 × 10 6 m / s . (c) Using De Broglie's wavelength equation, λ = h P , we get λ = 6 . 6 × 10 - 34 5 . 91 × 10 - 24 = 1 . 116 × 10 - 10 m = 0 . 112 nm ∴ De Broglie's wavelength of the electron is 0.112 nm. Here, the symbols have their usual meaning.

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According to Einstein's photoelectric equation, the graph between the maximum kinetic energy of photoelectrons ejected and the frequency of incident radiation is

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 23

Light of frequency

7.21 \times 10^{14} H z

is incident on a metal surface. Electrons with maximum speed of

6 \times 10^{5} m s^{- 1}

are ejected from the surface. The threshold frequency for photoemission of electrons is (Given

h = 6.63 \times 10^{- 34} J s, m_{e} = 9.1 \times 10^{- 31} k g

)

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 24

The photoelectric threshold wavelength for silver is

λ_{0}

. The energy of the electron ejected from the surface of silver by an incident wavelength

λ (λ < λ_{0})

will be

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 25

A metallic surface is irradiated by a monochromatic light of frequency

υ_{1}

and stopping potential is found to be

V_{1}

. If the light of frequency

υ_{2}

irradiates the surface, the stopping potential will be

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 26

According to Einstein's photoelectric equation, the graph of kinetic energy of the photoelectron emitted from the metal versus the frequency of the incident radiation gives a straight line graph, whose slope

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 27

The photoelectric cut-off voltage in a certain experiment is $1.5 V$ . What is the maximum kinetic energy of photoelectrons emitted? Take, $e = 1.6 \times 10^{- 19} C$

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 28

Light of wavelength

488 nm

is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is

0.38 V

. Find the work function of the material from which the emitter is made.

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 29

The threshold frequency for a certain metal is

3.3 \times 10^{14} Hz

. If light of frequency

8.2 \times 10^{14} Hz

is incident on the metal, predict the cutoff voltage for the photoelectric emission.

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Physics Crash Course (Based on Revised Syllabus - 2023)>Chapter 11 - DUAL NATURE OF RADIATION AND MATTER>Exercise>Q 30

What is the

(a) momentum,

(b) speed, and

According to Einstein's photoelectric equation, the graph between the maximum kinetic energy of photoelectrons ejected and the frequency of incident radiation is

Important Questions on DUAL NATURE OF RADIATION AND MATTER

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