Question

A monochromatic source emitting light of 600 nm, has a power output of 66 W. The number of photons emitted by the source per second is (Given, Plank's constant h = 6.6 \(\times\) 10\(^{-34}\) Js)

• A. 2 \(\times\) 10\(^{18}\)
• B. 2 \(\times\) 10\(^{19}\)
• C. 2 \(\times\) 10\(^{20}\)
• D. 8 \(\times\) 10\(^{22}\)

Hint:

Number of photons per second = P / (hc/wavelength).

Answer 1

The Correct Option is C

Step 1: Frequency First:
Find the frequency of the light from the wavelength. \[ f = \frac{c}{\lambda} = \frac{3 \times 10^{8}}{6 \times 10^{-7}} = 5 \times 10^{14} \text{ Hz} \]

Step 2: Energy Per Photon:
\[ E = h f = 6.6 \times 10^{-34} \times 5 \times 10^{14} = 3.3 \times 10^{-19} \text{ J} \]

Step 3: Photons Per Second:
In one second the source releases 66 J. So \[ n = \frac{66 \text{ J}}{3.3 \times 10^{-19} \text{ J}} = 20 \times 10^{19} = 2 \times 10^{20} \]

Step 4: Match the Option:
The value \(2 \times 10^{20}\) is option 3. The other options differ by at least a factor of 10, so they do not fit.

Final Answer:
\[\boxed{2 \times 10^{20}}\]