Q2 / 160 · TS EAMCET 2008 · Chemistry
The velocities of two particles $A$ and $B$ are 0.05 and $0.02 \mathrm{~ms}^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is
- Correct answerA$2: 1$
- B$1: 4$
- C$1: 1$
- D$4: 1$
Solution
Given, velocity of particle $A=0.05 \mathrm{~ms}^{-1}$
Velocity of particle $B=0.02 \mathrm{~ms}^{-1}$
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 $A$
$$
\lambda_A=\frac{h}{x \times 0.05}
$$
For particle $B$
$$
\lambda_B=\frac{h}{5 x \times 0.02}
$$
Eq (i)/(ii)
$$
\frac{\lambda_A}{\lambda_B}=\frac{5 x \times 0.02}{x \times 0.05}
$$
$\begin{aligned} \frac{\lambda_A}{\lambda_B} & =\frac{2}{1} \\ \text { or } & 2: 1\end{aligned}$
Hence, the correct answer is option: 'A'.