If a source of electromagnetic radiation having power 15 kW produces 10¹⁶ photons per second, the radiation belongs to a part of spectrum is.
(Take Planck constant h=6 × 10⁻³⁴ Js )

Solution

Physics sir · 2 steps

Divide the power by the photons per second to get one photon's energy, then let its frequency name the region.

1. Energy per photon. Power is energy delivered per second, and 10¹⁶ photons share it every second. So each photon carries E = P/n = (15 × 10³)/10¹⁶ = 1.5 × 10⁻¹² J.

   ν = E/h = (1.5 × 10⁻¹²)/(6 × 10⁻³⁴) = 2.5 × 10²¹ Hz

   Region	Typical frequency	Does 2.5 × 10²¹ Hz fit?
   Radio waves	below about 10⁹ Hz	No, far too low
   Microwaves	10⁹ to 10¹² Hz	No, far too low
   Ultraviolet	10¹⁵ to 10¹⁷ Hz	No, still too low
   Gamma rays	above about 10¹⁹ Hz	Yes

2. So. Each photon has about 9.4 MeV of energy and a frequency of 2.5 × 10²¹ Hz. That puts the radiation among the gamma rays, option (a).

The idea to keep. Power divided by photons per second gives the energy of one photon. Then ν = E/h, and the frequency tells you the region. High power with few photons means very energetic photons.

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