Question

What should be the velocity of an electron so that its momentum becomes equal to that of a photon of wavelength 5200 $\mathring{A} $?

• A. 700 $ ms^{ - 1} $
• B. 1000 $ ms^{ - 1} $
• C. 1400 $ ms^{ - 1} $
• D. 2800 $ ms^{ - 1} $

Answer 1

Answer: (C)

Momentum, p = mv = $ \frac{ h }{ \lambda} $
$ v = \frac{ h }{ m \lambda} $
$\therefore v = \frac{ 6.62 \times 10^{ - 34}}{ 9.1 \times 10^{ - 31 } \times 5.2 \times 10^{ - 7 }} $
$ \Rightarrow v = \frac{ 6.62 \times 10^4 }{ 9.1 \times 5.2 } $
$ \Rightarrow v = 1.4 \times 10^3 \, ms^{ - 1} $
$ \Rightarrow v = 1400 \, ms^{ - 1} $