Question

Which of the following particle having same kinetic energy, would have the maximum de-Broglie wave length
a) α-particle
b) proton
c) β-particle
d) neutron

Answer 1

c. because of inverse relation of wavelength with mass

Answer 2

Hey.

Here is the answer.

The deBroglie wave length of a particle = h/p,

Where,

h= Planck's Constant,

p = momentum of the particle.

Momentum and kinetic energy of a particle are related and momentum p =√(2mE).

Since kinetic energy of the particles is the same, therefore, the heavier the particle, more its momentum and larger the momentum, shorter the deBroglie wave length.

According, the shortest wavelength shall be of the alpha particle. The wave length of the proton will be about 4 times that of the alpha particle ( mass of an alpha particle= about 4 times mass of a proton).

The mass of neutron and proton is almost same so wavelength will also be similar .

A bita particle is an electron with mass 5.5×10^-4 amu which is far less than alpha particle.

So , The wavelength of bita particle will be largest.


Thanks.