Question

A particle of mass 1 mg has the same
wavelength as an electron moving with a
velocity of $3\times {10}^{6}m{s}^{-1}$
The velocity of the
particle is :
$(massofelectron=9.1\times {10}^{-31}kg)$

• A. $3\times {10}^{-31}m{s}^{-1}$
• B. $2.7\times {10}^{-21}m{s}^{-1}$
• C. $2.7\times {10}^{-18}m{s}^{-1}$
• D. $9\times {10}^{-2}m{s}^{-1}$

Answer 1

The correct option is C $2.7\times {10}^{-18}m{s}^{-1}$

de-Broglie wavelength associated with electron
moving with velocity ,
$\lambda =\frac{h}{mv}$
so, ${\lambda }_e=\frac{h}{9.1\times {10}^{-31}\times 3\times {10}^6}$
Wavelength of particle of mass 1 mg moving with velocity .
${\lambda }_p=\frac{h}{{10}^{-3}\times v}$
As given,${\lambda }_e={\lambda }_p$
$\Rightarrow \frac{h}{{10}^{-3}\times v}=\frac{h}{9.1\times {10}^{-31}\times 3\times {10}^6}$
$v=\frac{27.3\times {10}^{-25}}{{10}^{-3}}m/s=2.73\times {10}^{-21}m/s$