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Question -

An electron and a photoneach have a wavelength of 1.00 nm. Find

(a) their momenta,

(b) the energy of thephoton, and

(c) the kinetic energy of electron.



Answer -

Wavelength of an electron 

= 1 × 10−9 m

Planck’s constant, h = 6.63× 10−34 Js

(a) The momentum of anelementary particle is given by de Broglie relation:

It is clear that momentumdepends only on the wavelength of the particle. Since the wavelengths of anelectron and a photon are equal, both have an equal momentum.

(b) The energy of aphoton is given by the relation:

Where,

Speed of light, c = 3 × 108 m/s

Therefore, the energy ofthe photon is 1.243 keV.

(c) The kinetic energy (K)of an electron having momentum p,is given by the relation:

Where,

m = Mass of the electron = 9.1 × 10−31 kg

= 6.63 × 10−25 kg m s−1                                                                     

Hence,the kinetic energy of the electron is 1.51 eV.













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