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Dual Nature of Radiation question

2025 · 23 Jan · Shift 1 · Q54
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  5. /2025 · 23 Jan · Shift 1 · Q54

Dual Nature of Radiation question

2025 · 23 Jan · Shift 1 · Q54

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
A sub-atomic particle of mass 10−30 kg10^{-30} \mathrm{~kg}10−30 kg is moving with a velocity 2.21×106 m/s2.21 \times 10^6 \mathrm{~m} / \mathrm{s}2.21×106 m/s. Under the matter wave consideration, the particle will behave closely like (h=6.63×10−34 J.s)\qquad\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)(h=6.63×10−34 J.s)
  1. A
    X-rays
  2. B
    Infra-red radiation
  3. C
    Gamma rays
  4. D
    Visible radiation
View written solutionFree

Correct answer: A

  1. Use de Broglie wavelength formula

For a particle of mass mmm moving with speed vvv, the matter-wave wavelength is

λ=hmv\lambda = \frac{h}{mv}λ=mvh​

Given:

m=10−30 kg,v=2.21×106 m/s,h=6.63×10−34 J⋅sm = 10^{-30}\,\text{kg}, \qquad v = 2.21\times 10^6\,\text{m/s}, \qquad h = 6.63\times 10^{-34}\,\text{J·s}m=10−30kg,v=2.21×106m/s,h=6.63×10−34J⋅s
  1. Calculate momentum
p=mv=10−30×2.21×106=2.21×10−24 kg m/sp = mv = 10^{-30}\times 2.21\times 10^6 = 2.21\times 10^{-24}\,\text{kg m/s}p=mv=10−30×2.21×106=2.21×10−24kg m/s
  1. Calculate de Broglie wavelength
λ=6.63×10−342.21×10−24\lambda = \frac{6.63\times 10^{-34}}{2.21\times 10^{-24}}λ=2.21×10−246.63×10−34​ λ=3.0×10−10 m\lambda = 3.0\times 10^{-10}\,\text{m}λ=3.0×10−10m
  1. Compare with electromagnetic spectrum
3.0×10−10 m=0.3 nm=3 A˚3.0\times 10^{-10}\,\text{m} = 0.3\,\text{nm} = 3\,\text{Å}3.0×10−10m=0.3nm=3A˚

Typical wavelength ranges:

  • X-rays: about 10−1110^{-11}10−11 to 10−8 m10^{-8}\,\text{m}10−8m
  • Visible light: about 4×10−74\times 10^{-7}4×10−7 to 7×10−7 m7\times 10^{-7}\,\text{m}7×10−7m
  • Infra-red: longer than visible
  • Gamma rays: usually less than about 10−11 m10^{-11}\,\text{m}10−11m

Since λ=3.0×10−10 m\lambda = 3.0\times 10^{-10}\,\text{m}λ=3.0×10−10m lies in the X-ray region, the particle behaves closely like X-rays.

  1. Option check
  • A: X-rays →\rightarrow→ Correct
  • B: Infra-red radiation →\rightarrow→ Incorrect
  • C: Gamma rays →\rightarrow→ Incorrect
  • D: Visible radiation →\rightarrow→ Incorrect

Therefore, the correct answer is A.

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