Aparticle with mass m and charge e is accelerated through a potential difference (v). what is the wavelength of the particle?

The wavelength of the particle is

Explanation:

We know that after accelerating across a potential 'V' the potential energy of the charge is converted into kinetic energy as

now according to De-Broglie theory the wavelength associated with a particle of mass 'm' moving with a speed of 'v' is given by

where

'h' is planck's constant

'm' is the mass of particle

'v' is the velocity of the particle

Applying the values in the above equation we get

Thus

Wavelength of the particle is

Solution:

As per the question:

The particle with mass, m and charge, e accelerates through V (potential difference).

The momentum of the particle, if it travels with velocity, :

Now, squaring both sides and dividing by 2.

Also,

         (1)

Now, we know that Kinetic energy of particle accelerated through V:

K.E = eV       (2)

where

e = electronic charge =

From eqn (1) and (2):

             (3)

From eqn (2) and (3):

From the de-Broglie relation:

     (4)

where

= wavelength of particle

h = Planck's constant

From eqn (3) and (4):

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explanation:

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