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Dual Nature of Radiation question

2025 · 22 Jan · Shift 1 · Q57
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Dual Nature of Radiation question

2025 · 22 Jan · Shift 1 · Q57

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of
  1. A
    Both Cs and Li
  2. B
    Neither Cs nor Li
  3. C
    Li only
  4. D
    Cs only
View written solutionFree

Correct answer: D

  1. Use the photoelectric condition

    Photoelectric emission is possible only if the photon energy is at least equal to the work function: Eγ≥ϕE_\gamma \ge \phiEγ​≥ϕ

  2. Calculate the energy of incident light

    Given wavelength: λ=550 nm\lambda = 550\,\text{nm}λ=550nm

    Photon energy in eV is: Eγ=1240λ(nm)E_\gamma = \frac{1240}{\lambda(\text{nm})}Eγ​=λ(nm)1240​

    So, Eγ=1240550≈2.25 eVE_\gamma = \frac{1240}{550} \approx 2.25\,\text{eV}Eγ​=5501240​≈2.25eV

  3. Compare with work functions

    • For cesium (Cs): ϕCs=1.9 eV\phi_{\text{Cs}} = 1.9\,\text{eV}ϕCs​=1.9eV Since 2.25>1.92.25 > 1.92.25>1.9 photoelectric effect is possible.

    • For lithium (Li): ϕLi=2.5 eV\phi_{\text{Li}} = 2.5\,\text{eV}ϕLi​=2.5eV Since 2.25<2.52.25 < 2.52.25<2.5 photoelectric effect is not possible.

  4. Evaluate options

    • A: Both Cs and Li → Incorrect
    • B: Neither Cs nor Li → Incorrect
    • C: Li only → Incorrect
    • D: Cs only → Correct

  5. Final answer

    Photoelectric effect occurs only for cesium.

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