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Question

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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Solution

Given: The wavelength of the electron and photon is 1.00nm.

(a)

The momentum of a particle is given as,

p= h λ

Where, the wavelength is λ, Planck’s constant is h and the momentum of a photon is p.

By substituting the given values in the above formula, we get

p= 6.63× 10 34 1× 10 9 =6.63× 10 25 kg ms -1

Thus, the momentum of electron and photon is 6.63× 10 25 kg ms -1 .

(b)

The energy of the photon is given as,

E= hc λ

Where, the energy of a photon is E and the speed of light is c.

By substituting the given values in above formula, we get

E= 6.63× 10 34 ×3× 10 8 1× 10 9 ×1.6× 10 19 =1243.1eV =1.2431keV

Thus, the energy of the photon is 1.2431keV.

(c)

The kinetic energy of an electron is given as,

K= 1 2 p 2 m

Where, the momentum of a electron is p, the mass of the electron is m and the kinetic energy of an electron is K.

By substituting the given values in above formula, we get

K= 1 2 × ( 6.63× 10 25 ) 2 9.1× 10 31 =2.415× 10 19 J = 2.415× 10 19 1.6× 10 19 =1.51eV

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


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