A monochromatic source of light operating at \(15\) kW emits \(2.5\times 10^{22}\) photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take \(h=6.6\times 10^{-34}\) J·s and \(c=3\times 10^8\) m/s).

Power of the source, \(P = 15 \text{ kW} = 15 \times 10^3 \text{ J/s}\)

Number of photons emitted per second, \(n = 2.5 \times 10^{22} \text{ s}^{-1}\)

Energy of one photon, \(E = \dfrac{P}{n} = \dfrac{15 \times 10^3}{2.5 \times 10^{22}} = 6 \times 10^{-19} \text{ J}\)

Using \(E = \dfrac{hc}{\lambda}\), we get \(\lambda = \dfrac{hc}{E}\)

\(\lambda = \dfrac{6.6 \times 10^{-34} \times 3 \times 10^8}{6 \times 10^{-19}} = 3.3 \times 10^{-7} \text{ m} = 330 \text{ nm}\)

The wavelength \(330 \text{ nm}\) lies in the ultraviolet region of the electromagnetic spectrum.

Answer: Ultraviolet