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An electron and a photon each have a wavelength 1.00 nm. Find

(i)their momenta.

(ii)the energy of the photon and

(iii)the kinetic energy of electron.

Asked by Topperlearning User 21st May 2014, 12:48 PM
Answered by Expert
Answer:

Let, wavelength of an electron and a photon be λe and λp respectively.

λe =  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

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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.


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

Where,

Speed of light, c = 3 × 108 m/s

 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:

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Where, 

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

p = 6.63 × 10–25 kg m s–1


Hence, kinetic energy of the electron is 1.51 eV.

 

 

Answered by Expert 21st May 2014, 2:48 PM
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