Question

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 ________.

• A. Microwave
• B. Infrared
• C. Visible
• D. Ultraviolet

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The power of a light source is the energy emitted per unit time. For a stream of photons, power is the product of the number of photons emitted per second ($n$) and the energy of a single photon ($E = h\nu$ or $E = hc/\lambda$).
Step 2: Key Formula or Approach:
1. Power $P = n \times E_{photon} = n \times \frac{hc}{\lambda}$.
2. Rearrange to find wavelength: $\lambda = \frac{nhc}{P}$.
Step 3: Detailed Explanation:
Given $P = 15 \text{ kW} = 15 \times 10^3 \text{ W}$, $n = 2.5 \times 10^{22} \text{ photons/s}$. \[ \lambda = \frac{(2.5 \times 10^{22}) \times (6.6 \times 10^{-34}) \times (3 \times 10^8)}{15 \times 10^3} \] \[ \lambda = \frac{2.5 \times 6.6 \times 3 \times 10^{22-34+8}}{15 \times 10^3} = \frac{49.5 \times 10^{-4}}{15 \times 10^3} \] \[ \lambda = 3.3 \times 10^{-7} \text{ m} = 330 \text{ nm} \] The visible spectrum ranges from approximately 400 nm to 700 nm. A wavelength of 330 nm lies just below the visible range (violet), placing it in the ultraviolet region.
Step 4: Final Answer:
The radiation belongs to the Ultraviolet region.