According to de-Broglie hypothesis, the wavelength associated with moving electron of mass 'm' is `'lambda_(e)'`. Using mass energy relation and Planck's quantum theory, the wavelength associated with photon is `'lambda_(p)'`. If the energy (E) of electron and photonm is same, then relation between `lambda_e` and `'lambda_(p)'` is

Options

A. `lamda_p prop lamda_e`
B. `lamda_p prop lamda_e^2`
C. `lamda_p prop sqrtlamda_e`
D. `lamda_p prop 1/lamda_e`

Answer

A

Explanation

Using mass energy relation , for the electron
`E = mc^2 = (mc), c = pc (therefore p=mc)`
`therefore p= E/c`
`therefore lamda_e = (h)/(mv) = h/p = (hc)/(E ) " "…(1)`
and as per planck's quantum theory ,
For a photon `E = hv = (hc)/(lamda_p)`
`therefore lamda_p = (hc)/(E ) " " ..(2)`
`therefore` From (1) and (2)
`therefore lamda_p = lamda_e " or " lamda_p prop lamda_e`
[Out of the four option, this is the nearest option ]