Question

If a photon and an electron have same de-broglie wavelength, then

• A. Both have same kinetic energy
• B. Proton has more K.E. than electron
• C. Electron has more K.E. than proton
• D. Both have same velocity

Answer 1

The correct option is C Electron has more K.E. than proton

De Broglie wavelength is given by:

$\lambda =\frac{h}{p}$

$p=\sqrt{2Em}$ Where E is kinetic energy.
Given that both the electron and proton have the same De Broglie wavelength.
Then $p_e=p_p$

$E_{electron}{m}_{electron}=E_{proton}{m}_{proton}$

$\frac{E_{electron}}{E_{proton}}=\frac{m_{proton}}{m_{electron}}$

and we know that:

$\frac{m_{proton}}{m_{electron}}>1$

Hence $E_{electron}>E_{proton}$