Question

The velocities of two particles $A$ and $B$ are $0.05$ and $0.02\, ms^{-1}$ 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 $A=0.05\, ms ^{-1}$
Velocity of particle $B=0.02\, ms ^{-1}$
Let the mass of particle $A=x$
$\therefore $ The mass of particle $B=5 x$
de-Broglie's equation is
$\lambda=\frac{h}{m v}$
For particle $A$
$\lambda_{A}=\frac{h}{x \times 0.05} ...(i)$
For particle B
$\lambda=\frac{h}{5 x \times 0.02}...(ii)$
Eq (i)/(ii)
$\frac{\lambda_{A}}{\lambda_{B}}=\frac{5 x \times 0.02}{x \times 0.05}$
$\frac{\lambda_{A}}{\lambda_{B}}=\frac{2}{1}$
Or $2: 1$