Q6 / 100 · BITSAT 2024 (Memory Based Paper 3) · Chemistry
If the de-broglie wavelength of a particle of mass $(m)$ is 100 times its velocity. Then, its value in terms of its mass $(m)$ and plank constant $(h)$ is
- A$\frac{1}{10} \sqrt{\frac{m}{h}}$
- Correct answerB$10 \sqrt{\frac{h}{m}}$
- C$\frac{1}{10} \sqrt{\frac{h}{m}}$
- D$10 \sqrt{\frac{m}{h}}$
Solution
Let the wavelength of given particle $=x$
Velocity $(v)=\frac{x}{100}$
Using wavelength formula
$\begin{aligned}
\lambda = \frac{h}{m v} \\
\therefore & x =\frac{h}{m\left(\frac{x}{100}\right)} \\
x & =\frac{100 h}{m x} \\
x^2 & =100 \frac{h}{m} \\
\Rightarrow \quad x & =10 \sqrt{\frac{h}{m}}
\end{aligned}$
Hence, the correct answer is option: 'B'.