Question

For which of the following particles will it be most difficult to experimentally verify the de-Broglie relationship?
A. An electron
B. A proton
C. An $\alpha -$ particle
D. A dust particle

Answer 1

de-Broglie wavelength is given by the relation $\lambda = \dfrac{h}{{mv}}$. So if m increases, $\lambda$ will decrease. So look out for the subatomic particles in the given options for which de-Broglie relation holds good.

Complete answer:
If a material particle of mass m is moving with velocity v, then momentum of the particle is $p = mv$ . According to de-Broglie hypothesis, the wavelength of wave associated with the moving material particle is $\lambda = \dfrac{h}{p} = \dfrac{h}{{mv}}$, where h is the Planck’s constant. From this relation, we can see that the de-Broglie wavelength is inversely proportional to the mass of the particle. If the mass of a particle increases, the de-Broglie wavelength becomes small. So, de-Broglie relation can be verified to a good-extent for subatomic particles. In the given options, an electron, a proton and an article are subatomic particles whose mass is very-very small. On the other hand the mass of a dust particle is too large as compared to these particles. Also, the motion of a dust particle is also not linear. So, de-Broglie relation does not hold good for a dust particle.

So, the correct answer is “Option A”.

Note:
According to de-Broglie a moving particle sometimes acts as a wave and sometimes as a particle or a wave is associated with the moving particle which controls the particle in every respect. The wave associated with the moving particle is called the matter wave or de-Broglie wave whose wavelength is called the de-Broglie wavelength.