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Monochromatic radiation emitted when an electron in a hydrogen atom jumps from the first excited state to the ground state irradiates a photosensitive material. The stopping potential is measured to be 3.57 V. The threshold frequency of the material is:

Asked in AIPMT 2012 · Threshold frequency

Answer: (3) 1.6×10¹⁵ Hz

Step-by-step solution

Energy levels of hydrogen: Eₙ=-(13.6)/(n²) eV.

Ground state E₁=-13.6 eV, first excited state E₂=-3.4 eV.

Photon emitted in the jump: h u=E₂-E₁=-3.4-(-13.6)=10.2 eV.

The stopping potential gives the maximum kinetic energy: Kₘₐₓ=eVₛ=3.57 eV.

Work function: φ₀=h u-Kₘₐₓ=10.2-3.57=6.63 eV.

Threshold frequency: u₀=(φ₀)/h=(6.63×1.6×10⁻¹⁹)/(6.63×10⁻³⁴)=1.6×10¹⁵ Hz.

Why the other options are wrong

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