Question

If m is the mass of an electron and c is the speed of light , The ration of the wavelength of photon of energy E to that to the electron of the same energy is ;

• A. $c\sqrt{\frac{2m}{E}}$
• B. $\sqrt{\frac{2m}{E}}$
• C. $\sqrt{\frac{2m}{cE}}$
• D. $\sqrt{\frac{m}{E}}$

Answer 1

Answer: (A)

$c\sqrt{\frac{2m}{E}}$

Answer 2

: Energy of photon $E = h\upsilon = \frac{hc}{\lambda_{ph}}$

Where $\lambda_{ph}$is the wave length of a photon

$\lambda_{ph} = \frac{hc}{E}$

Wavelength of the electron,

$\lambda_{e} = \frac{h}{\sqrt{2mE}}$

$\therefore\frac{\lambda_{ph}}{\lambda_{e}} = \frac{hc}{E} \times \frac{\sqrt{2mE}}{h} = c\frac{\sqrt{2m}}{E}$