Question

What are matter waves? Find the ratio of de Broglie wavelengths associated with proton and alpha particles when both particles 

(a) Are accelerated through the same potential difference. 

(b) Have same velocity.

Answer 1

• Matter wave represents the probability of finding a particle in space. 

• Matter waves are not electromagnetic in nature. 

• De-Brogile or matter wave is independent of the charge on the material particle. 

(a) The de-Broglie wavelength of a particle of mass m and moving with velocity v is given by

De-Broglie wavelength of a proton of mass m₁ and kinetic energy k is given by

For an alpha particle mass m₂ carrying charge q_o is accelerated through potential V, then

The ratio of corresponding wavelength, from Eq. (i) and (ii), we get