JEE Main 2025 Jan 23 Shift 1, Physics Q4: Wave Nature of Matter

JEE Main2025Jan 23, Shift 1Physics

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
C
Gamma rays
D
Visible radiation

Solution

The de Broglie wavelength is $λ = \frac{h}{p} = \frac{h}{m v}$ .

$λ = \frac{6.63 \times 1 0 ^{- 34}}{1 0 ^{- 30} \times 2.21 \times 1 0 ^{6}} = 3 \times 1 0^{- 10}$ m $= 3$ Å.

A wavelength of order $1 0^{- 10}$ m falls in the X-ray region of the electromagnetic spectrum (gamma rays are $< 1 0^{- 11}$ m, visible light is $\sim 1 0^{- 7}$ m, infra-red is even longer).

$∴$ The matter wave behaves like X-rays.

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JEE Main 2025 Jan 23 Shift 1, Physics Q4: Wave Nature of Matter

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