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Dual Nature of Radiation question

2024 · 6 Apr · Shift 2 · Q69
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Dual Nature of Radiation question

2024 · 6 Apr · Shift 2 · Q69

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
When UV light of wavelength 300 nm300 \mathrm{~nm}300 nm is incident on the metal surface having work function 2.13 eV2.13 \mathrm{~eV}2.13 eV, electron emission takes place. The stopping potential is : (Given hc =1240 eV nm=1240 \mathrm{~eV} \mathrm{~nm}=1240 eV nm )
  1. A
    4 V
  2. B
    2 V
  3. C
    4.1 V
  4. D
    1.5 V
View written solutionFree

Correct answer: B

  1. Use Einstein’s photoelectric equation

    Kmax⁡=hν−ϕK_{\max} = h\nu - \phiKmax​=hν−ϕ

    In electron-volt form,

    Kmax⁡(eV)=hcλ−ϕK_{\max}(\text{eV}) = \frac{hc}{\lambda} - \phiKmax​(eV)=λhc​−ϕ

    Given:

    • λ=300 nm\lambda = 300\,\text{nm}λ=300nm
    • ϕ=2.13 eV\phi = 2.13\,\text{eV}ϕ=2.13eV
    • hc=1240 eV⋅nmhc = 1240\,\text{eV·nm}hc=1240eV⋅nm
  2. Calculate the energy of the incident photon

    E=hcλ=1240300 eVE = \frac{hc}{\lambda} = \frac{1240}{300}\,\text{eV}E=λhc​=3001240​eV

    E=4.133 eVE = 4.133\,\text{eV}E=4.133eV

  3. Find the maximum kinetic energy of emitted electrons

    Kmax⁡=4.133−2.13=2.003 eVK_{\max} = 4.133 - 2.13 = 2.003\,\text{eV}Kmax​=4.133−2.13=2.003eV

    Kmax⁡≈2.0 eVK_{\max} \approx 2.0\,\text{eV}Kmax​≈2.0eV

  4. Relate kinetic energy to stopping potential

    eV0=Kmax⁡eV_0 = K_{\max}eV0​=Kmax​

    Since Kmax⁡K_{\max}Kmax​ is in eV, the stopping potential in volts is numerically equal:

    V0≈2.0 VV_0 \approx 2.0\,\text{V}V0​≈2.0V

  5. Check options

    • A: 4 V4\,\text{V}4V ❌
    • B: 2 V2\,\text{V}2V ✅
    • C: 4.1 V4.1\,\text{V}4.1V ❌
    • D: 1.5 V1.5\,\text{V}1.5V ❌

Therefore, the correct option is B.

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