Question

The velocities of two particles $A$ and $B$ are $0.05$ and $0.02m{s}^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de- Broglie's wavelength is

• A. 2 : 1
• B. -1 : 4
• C. 1 : 1
• D. 4 : 1

Answer 1

Answer: (A)

Given, velocity of particle $A=0.05m{s}^{-1}$
Velocity of particle $B=0.02m{s}^{-1}$
Let the mass of particle $A=x$
$\therefore$ The mass of particle $B=5x$
de-Broglie's equation is
$\lambda =\frac{h}{mv}$
For particle $A$
${\lambda }_A=\frac{h}{x\times 0.05}...(i)$
For particle B
$\lambda =\frac{h}{5x\times 0.02}...(ii)$
Eq (i)/(ii)
$\frac{{\lambda }_A}{{\lambda }_B}=\frac{5x\times 0.02}{x\times 0.05}$
$\frac{{\lambda }_A}{{\lambda }_B}=\frac{2}{1}$
Or $2:1$