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When a certain photosensitive surface is illuminated with monochromatic light of frequency u, the stopping potential for the photocurrent is -(V₀)/2. When the surface is illuminated by monochromatic light of frequency u/2, the stopping potential is -V₀. The threshold frequency for photoelectric emission is

Asked in JEE Main 12th Jan 2nd Shift 2019 · Threshold frequency

Answer: (4) (3 u)/2

Step-by-step solution

h u=φ+(eV₀)/2 and hu/2=φ+eV₀.

Multiply the first by 2: 2h u=2φ+eV₀.

Subtract the second: 2h u-(h u)/2=φ, so φ=3/2h u.

u₀=φ/h=(3 u)/2.

Note that this threshold is above the incident frequency u, so the data as printed are not physically consistent; see DEFECTS.

Why the other options are wrong

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