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: Understanding the Question:
A source gives out 66 J of light energy every second. Each photon carries a fixed energy that depends on the wavelength. We need the number of photons per second.

Step 2: Key Formula or Approach:
Energy of one photon: \(E = \dfrac{hc}{\lambda}\). Power is total energy per second, so \[ P = n E \quad \Rightarrow \quad n = \frac{P}{E} = \frac{P\lambda}{hc} \] where n is the number of photons per second.

Step 3: Energy of One Photon:
\(\lambda = 600 \text{ nm} = 6 \times 10^{-7}\) m and \(c = 3 \times 10^{8}\) m/s. \[ E = \frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{6 \times 10^{-7}} = 3.3 \times 10^{-19} \text{ J} \]

Step 4: Number of Photons:
\[ n = \frac{66}{3.3 \times 10^{-19}} = 2 \times 10^{20} \text{ per second} \]

Step 5: Checking Each Option:
Option 1 (\(2 \times 10^{18}\)) and option 2 (\(2 \times 10^{19}\)) are too small by factors of 100 and 10.
Option 4 (\(8 \times 10^{22}\)) is far too large.
Option 3 (\(2 \times 10^{20}\)) matches our result.

Final Answer:
The source emits \(2 \times 10^{20}\) photons every second, which is option 3. \[ \boxed{2 \times 10^{20}} \]