The wavelength `lambda_(e)` of an electron and `lambda_(P)` of a photon of same energy E are related by:

Options

A. `lambda_(p)proplambda_(e)^(2)`
B. `lambda_(p)proplambda_(e)`
C. `lambda_(p) prop sqrt(lambda_(e))`
D. `lambda_(p)prop(1)/(sqrt(lambda_(e)))`

Answer

A

Explanation

Wavelength of electron,
`lambda_(e)=(h)/(sqrt(2mE))`
`therefore lambda_(e)^(2)=(h^(2))/(2mE) therefore E=(h^(2))/(2mlambda_(e)^(2))`
Wavelength of photon,
`lambda_(p)=(hc)/(E )=(hc)/((h^(2))/(2mlambdae^(2)))=(2mclambda_(e)^(2))/(h)`
`therefore lambda_(p) prop lambda_(2)^(2) [because (2mc)/(h)="constant"]`