A sub-atomic particle of mass $10^{-30} \mathrm{~kg}$ is moving with a velocity $2.21 \times 10^6…

A sub-atomic particle of mass $10^{-30} \mathrm{~kg}$ is moving with a velocity $2.21 \times 10^6 \mathrm{~m} / \mathrm{s}$. Under the matter wave consideration, the particle will behave closely like _________ $\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J}. \mathrm{s}\right)$
  1. Visible radiation
  2. Gamma rays
  3. Infra-red radiation
  4. X-rays

Solution

$\begin{aligned}
& \lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{6.63 \times 10^{-34}}{10^{-30} \times 2.21 \times 10^6} \\ & =3 \times 10^{-10} \mathrm{~m}
\end{aligned}$
Hence particle will behave as x-ray.

Asked in: JEE Main 2025 (23 Jan Shift 1)

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