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(D) The power $P$ is given by $P = n E_{photon} = n \frac{hc}{\lambda}$, where $n$ is the number of photons emitted per second.Rearranging the formula

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Ultraviolet

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(D) The power $P$ is given by $P = n E_{photon} = n \frac{hc}{\lambda}$, where $n$ is the number of photons emitted per second.Rearranging the formula to solve for wavelength $\lambda$, we get $\lambda = \frac{nhc}{P}$.Substituting the given values: $n = 2.5 	imes 10^{22} 	ext{ s}^{-1}$, $h = 6.6 	imes 10^{-34} 	ext{ J}\cdot	ext{s}$, $c = 3 	imes 10^8 	ext{ m/s}$, and $P = 15 	ext{ kW} = 15 	imes 10^3 	ext{ W}$.$\lambda = \frac{(2.5 	imes 10^{22}) 	imes (6.6 	imes 10^{-34}) 	imes (3 	imes 10^8)}{15 	imes 10^3} = \frac{49.5 	imes 10^{-4}}{15 	imes 10^3} = 3.3 	imes 10^{-7} 	ext{ m}$.Converting to nanometers: $3.3 	imes 10^{-7} 	ext{ m} = 330 	ext{ nm}$.The wavelength range for the ultraviolet region is approximately $10 	ext{ nm}$ to $400 	ext{ nm}$.Therefore, $330 	ext{ nm}$ falls in the Ultraviolet region.

List-$I$ (Electromagnetic waves)	List-$II$ (Wavelength)
$(a)$ $AM$ radio waves	$(i)$ $10^{-10} \, m$
$(b)$ Microwaves	$(ii)$ $10^{2} \, m$
$(c)$ Infrared radiations	$(iii)$ $10^{-2} \, m$
$(d)$ $X$-rays	$(iv)$ $10^{-4} \, m$

Similar Questions

The frequencies of $\gamma$-rays,$X$-rays,and ultraviolet radiations are $B, A,$ and $C$ respectively. Which of the following relations is correct?

If a source of $4 \ kW$ power emits $10^{20}$ photons/second,then this radiation belongs to which part of the electromagnetic spectrum?

Which one of the following has the minimum wavelength?

The correct match between the entries in column $I$ and column $II$ is:
$I$ (Radiation) | $II$ (Wavelength)
$(a)$ Microwave | $(i)$ $100 \, m$
$(b)$ Gamma rays | $(ii)$ $10^{-15} \, m$
$(c)$ $A.M.$ radio waves | $(iii)$ $10^{-10} \, m$
$(d)$ $X$-rays | $(iv)$ $10^{-3} \, m$

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