Class 12 Physics - Chapter Dual Nature Of Radiation And Matter NCERT Solutions | An electron and a photon each have a wav
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.
Wavelength of an electron (λe) and a photon (λp), λe = λp = λ = 1 nm = 1 × 10−9 m
Planck’s constant, h = 6.63 × 10−34 Js
(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 wavelengths of an electron and a photon are equal, both have an equal momentum.
∴ p = 6.63 x 10-34 / 1 x 10-9 = 6.63 x 10-25 kg m s-1
(b) The energy of a photon is given by the relation: E = hc/λ
Where,
Speed of light, c = 3 × 108 m/s
∴ E = 6.63 x 10-34 x 3 x 108 / 1 x 10-9 x 1.6 x 10-19 = 1243.1 eV
Therefore, the energy of the photon is 1.243 keV.
(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 × 10−31 kg
p = 6.63 × 10−25 kg m s−1
∴ K = 1/2 x (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.
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