A material particle with a rest mass m0 is moving with speed of light c. The de-Broglie wavelength associated is given by

Question

A material particle with a rest mass m0 is moving with speed of light c. The de-Broglie wavelength associated is given by (A)  ( h/ m0 c )  (B)  ( m0 c / h )  (C) zero (D) infinite

Tardigrade Admin · Accepted Answer

λ = ( h / mv) where, m = ( m0 / √ 1 - ( v2 ) c2 ) As v = c, then ⇒ m = ( m0 / √ 1 - ( c2 ) c2 ) = ( m0 / √ 1 - 1) = ( m0 / 0 ) ⇒ m = ∞ , Hence, λ = ( h / ∞) = 0

Q. A material particle with a rest mass $m_{0}$ is moving with speed of light c. The de-Broglie wavelength associated is given by

$\frac{h}{m _{0} c}$

$\frac{m _{0} c}{h}$

zero

infinite

$λ = \frac{h}{m v}$ where, m = $\frac{m _{0}}{1 - \frac{v ^{2}}{c ^{2}}}$
As v = c, then
$\Rightarrow m = \frac{m _{0}}{1 - \frac{c ^{2}}{c ^{2}}} = \frac{m _{0}}{1 - 1} = \frac{m _{0}}{0}$
$\Rightarrow m = \infty$ ,
Hence, $λ = \frac{h}{\infty} = 0$

Q. A material particle with a rest mass m0​ is moving with speed of light c. The de-Broglie wavelength associated is given by

m0​ch​

hm0​c​