A source of monochromatic light liberates 9 × 10²⁰ photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating at same power will be :

Solution

Physics sir · 3 steps

Same power, longer wavelength: each photon carries less energy, so the source must send out more of them.

1. Power and photons. Power is the energy sent out per second. If n photons leave each second, each with energy hc/λ, then P = nhc/λ.

   n = Pλ/hc ⇒ n ∝ λ at fixed P

2. Take the ratio. The power stays at 400 W, so n₂/n₁ = λ₂/λ₁ = 800/600 = 4/3. You do not need h or c at all.
3. So. n₂ = 4/3 × 9 × 10²⁰ = 12 × 10²⁰ photons per second, which is option (a).

The idea to keep. At fixed power, the number of photons per second is proportional to wavelength. Longer wavelength means weaker photons, so you need more of them to carry the same energy.

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