An electron, a proton and an alpha particle have kinetic energy of `16E,4E` and `E` respectively. What is the qualitavtive order of their de Broglie wavelengths :-

Options

A. `lambda_(e)gtlambda_(p)=lambda_(alpha)`
B. `lambda_(p)=lambda_(alpha)gtlambda_(e)`
C. `lambda_(p)gtlambda_(e)gtlambda_(alpha)`
D. `lambda_(alpha)ltlambda_(e)gtgt lambda_(alpha)`

Answer

A

Explanation

`lambda_(e):lambda_(p):lambda_(alpha)=(1)/sqrt(m_(e)1.6E):(1)/(sqrtm_(p),4E):(1)/(sqrtm_(alpha.E))`
Hence `lambda_(e):lambda_(p)=lambda_(alpha)`