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 $\_\_\_\_$ . ( $\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ )

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Modern Physics

A sub-atomic particle of mass

1 0^{- 30} kg

is moving with a velocity

2.21 \times 1 0^{6} m / s

. Under the matter wave consideration, the particle will behave closely like

____

. (

h = 6.63 \times 1 0^{- 34} J . s

)

(A)Infra-red radiation
(B)X-rays✓ Correct
(C)Gamma rays
(D)Visible radiation

Answer: (B)

Solution

The de Broglie wavelength is

λ = \frac{h}{p} = \frac{h}{m v}

λ = \frac{6.63 \times 1 0 ^{- 34}}{1 0 ^{- 30} \times 2.21 \times 1 0 ^{6}} = \frac{6.63 \times 1 0 ^{- 34}}{2.21 \times 1 0 ^{- 24}} = 3 \times 1 0^{- 10} m = 3 \overset{˚}{A}

Electromagnetic radiation with wavelength of a few angstroms falls in the X-ray band (roughly 0.1 Å to 100 Å), so the particle behaves like X-rays.

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Single correct option

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