The wavelength `lamda_(e)` of ann electron and `lamda_(p)` of a photon of same energy E are related by

Options

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

Answer

A

Explanation

Wavelength of electron,
`lamda_(e)=(h)/(sqrt(2mE)) and ` proton, `lamda_(p)=(hc)/(E)`
`implies lamda_(e)^(2)=(h^(2))/(2mE) or E=(hc)/(lamda_(p))`
`therefore lamda_(e)^(2)=(h^(2))/(2m*(hc)/(lamda_(p))) implies lamda_(e)^(2)=(h^(2))/(2mhc)lamda_(p) implies lamda_(e)^(2)proplamda_(p)`