Question

The de Broglie wavelength of a sand grain weighing 2 mg blown by a wind of 10 m/s is:

• A. $3.31\times {10}^{-29}m$
• B. $1.12\times {10}^{-29}m$
• C. $2.21\times {10}^{-29}m$
• D. $4.42\times {10}^{-29}m$

Answer 1

The correct option is A $3.31\times {10}^{-29}m$

Given :
$\text{mass of sand grains}\left(m\right)=2\times {10}^{-6}kg\text{speed of the wind}\left(v\right)=10m/sec$
We know,
$\text{Planck's constant}\left(h\right)=6.62\times {10}^{-34}Js$

Again,

$\text{de Broglie wavelength}\left(\lambda \right)=\frac{h}{mv}$$=\frac{6.62\times {10}^{-34}}{2\times {10}^{-6}\times 10}=3.31\times {10}^{-29}m$