Question

De Broglie wavelength of a particle moving with velocity 2.25 x 10⁸ m s⁻¹ is same as the wavelength of photon. The ratio of kinetic energy of the particle to the energy of photon is _________ . Velocity of light = 3 x 10⁸ m s⁻¹(A) 1/8
(B) 3/8
(C) 5/8
(D) 7/8

Answer 1

Answer:

(B) 3/8

Explanation:

Hope you have got it

Answer 2

Since the de-Broglie wavelength depends only on the momentum of particle, both electron and photon must have same momentum. Also, kinetic energy expression can be written as,

for particle,

         $k=\frac{1}{2} mv^{2}$ Also, $L=\frac{h}{mv}$

          $k=\frac{1}{2} \frac{h}{Lv}v^{2} = \frac{vh}{2L}$ ....(i)

for photon,

         $k=\frac{hc}{L}$ ....(ii)

• divide both equations ,(i)/(ii)

        $\frac{v}{2c}$ = $\frac{2.25*3*10^{8}}{2*3*10^{8} } =\frac{3}{8}$