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

Options

A. `lamda_p prop sqrt(lamda_e)`
B. `lamda_p prop 1/sqrt(lamda_e)`
C. `lamda_p prop lamda_e^2`
D. `lamda_p prop lamda_e`

Answer

C

Explanation

Wavelength of an electron of energy E is
`lamda_e =h/(sqrt(2m_eE))" "...(i)`
Wavelength of a photon of same energy E is
`lamda_p=(hc)/E " or " E=(hc)/lamda_p" "...(ii)`
Squaring both sides , of Eq. (i) , we get
`lamda_e^2=(h^2)/(2m_elamda_E)" or "E=(h^2)/(2m_elamda_e^2)" "...(iii)`
Equating (ii) and (iii) , we get
`lamda_e^2=(h^2)/(2m_elamda_e^2)" or " lamda_p=(2m_ec)/hlamda_e^2" or " lamda_pproplamda_e^2`