Class 12 Physics
CBSE and UP Board
Dual Nature of Radiation and Matter
Chapter-11 Exercise 11.16
NCERT Solutions for Class 12 Physics Chapter 11 Question-16
An electron and a photon each have a wavelength of 1.00 nm. Find (a) their momenta, (b) the energy of the photon, and (c) the kinetic energy of electron
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Wavelength of an electron (λe) and a photon (λp), λe = λp = 1 nm = 1 x 10⁻9 m
Planck’s constant, h = 6.63 x 10-34 Js
Ans (a).
The momentum of an elementary particle is given by de Broglie relation:
λ = h/p => p = h/λ
It is clear that momentum depends only on the wavelength of the particle. Since the wavelength of an electron and photon are equal, both have an equal momentum.
Therefore , p = 6.63 x 10⁻34 / ( 1 x 10⁻9)
= 6.63 x 10⁻²⁵ kg ms⁻¹
Ans (b).
The energy of a photon is given by the relation:
E = hc/λ
Where, Speed of light, c = 3 x 108 m/s ,
Therefore, E = (6.63 x 10⁻34 ) x (3 x 108 /(1 x 10⁻9) (1.6 x 10⁻¹⁹ )
=1243.1 eV = 1.243 kev
Therefore, the energy of the photon is 1.243 keV.
Ans (c).
The kinetic energy (K) of an electron having momentum p, is given by the relation:
K = 1/2 p²/m
Where,
m = Mass of the electron = 9.1 x 10-31 kg
p = 6.63 x 10-25 kg m s-1
Therefore , K = 1/2 ( 6.63 x 10-25 )² /( 9.1 x 10-31) = 2.415 x 10⁻¹⁹ J
= (2.415 x 10⁻¹⁹) /(1.6 x 10⁻¹⁹) = 1.51 eV
Hence, the kinetic energy of the electron is 1.51 eV.