The threshold wavelength for photoelectric emission from a material is 5500 Aᵒ. 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 :

Solution

Physics sir · 4 steps

Emission depends on the colour of the light, not on how many watts the lamp has.

1. Threshold condition. Electrons come out only if one photon carries at least the work function. That means the wavelength must be shorter than the threshold, λ < 5500 Å.

   E = hc/λ ≥ φ₀ = hc/λ₀ ⇒ λ ≤ λ₀

2. Check each lamp. Infra-red light has wavelengths above about 7000 Å, which is longer than 5500 Å, so its photons are too weak. Ultra-violet light is below about 4000 Å, so every UV photon has enough energy.
3. Role of power. The wattage sets only how many photons arrive each second, not the energy of each photon. A 75 W IR lamp still emits nothing, and a 10 W UV lamp still emits, just with fewer electrons per second.
4. So. Both UV lamps, C and D, cause emission, so the answer is (c).

The idea to keep. Frequency decides whether photoelectrons come out at all. Intensity or power only decides how many come out. Below threshold frequency, no amount of power helps.

Answer from the NTA final answer key. Solution by PrepWiser.