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Dual Nature of Radiation question

2023 · 29 Jan · Shift 1 · Q64
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  5. /2023 · 29 Jan · Shift 1 · Q64

Dual Nature of Radiation question

2023 · 29 Jan · Shift 1 · Q64

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
The threshold wavelength for photoelectric emission from a material is 5500 Ao\mathop A\limits^oAo​. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp B. 10 W infra-red lamp C. 75 W ultra-violet lamp D. 10 W ultra-violet lamp Choose the correct answer from the options given below :
  1. A
    C only
  2. B
    A and D only
  3. C
    C and D only
  4. D
    B and C only
View written solutionFree

Correct answer: C

  1. Given data

    The threshold wavelength is λ0=5500 A˚=5.5×10−7 m.\lambda_0 = 5500\,\text{\AA} = 5.5 \times 10^{-7}\,\text{m}.λ0​=5500A˚=5.5×10−7m.

  2. Condition for photoelectric emission

    Photoelectric emission occurs only if the incident radiation has wavelength λ<λ0,\lambda < \lambda_0,λ<λ0​, i.e. frequency greater than threshold frequency.

    • Ultra-violet light has wavelength smaller than visible light, hence typically λUV<5500 A˚.\lambda_{UV} < 5500\,\text{\AA}.λUV​<5500A˚. So UV radiation can cause emission.
    • Infra-red light has wavelength larger than visible light, hence λIR>5500 A˚.\lambda_{IR} > 5500\,\text{\AA}.λIR​>5500A˚. So IR radiation cannot cause emission.

  3. Effect of power of lamp

    The power of the lamp (10 W or 75 W) affects the intensity, i.e. number of photons emitted per second, but not the energy per photon at a given wavelength range.

    Therefore, whether emission occurs depends on the type of radiation (UV or IR), not on whether the lamp is 10 W or 75 W.

  4. Check each source

    • A. 75 W infra-red lamp: No emission
    • B. 10 W infra-red lamp: No emission
    • C. 75 W ultra-violet lamp: Emission occurs
    • D. 10 W ultra-violet lamp: Emission occurs

  5. Correct combination

    Photoelectrons will be emitted for C and D only.

    Hence the correct option is C.\boxed{\text{C}}.C​.

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