Question

What is the mass of a particle with a Wavelength of $3.313\, \mathring{A}$ moving with a speed of $2.0 \times 10^{8}\, ms ^{-1} $ ?

• A. $1.0 \times 10^{-28} \,kg$
• B. $2.0 \times 10^{-32} \,kg$
• C. $1.0 \times 10^{-32}\, kg$
• D. $2.0 \times 10^{-28} \,kg$

Answer 1

Answer: (C)

According to de-Broglie relation:

$\lambda=\frac{h}{m v}$

where, $h=$ Planck's constant $=6.626 \times 10^{-34} \,Js$

$v=$ speed of moving particle

$m=$ mass of moving particle

$\lambda=$ wavelength of particle.

Thus,

$m-\frac{h}{\lambda \times v}$

Given,

Speed (velocity) of moving particle $(v)=2 \times 10^{8} \,m / s$

Wavelength of moving particle $(\lambda)=3.313 \, \mathring{A}$

$=30313 \times 10^{-10}\,m$

$\therefore \, m=\frac{6.626 \times 10^{-34}}{3.313 \times 2 \times 10^{8} \times 10^{-10}}$

$m=1 \times 10^{-32}\, kg$