Question

The number of photons per second on average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3×10⁻³ watt will be : (h=6.6×10⁻³⁴ Js)

• A. 10¹⁵
• B. 10¹⁸
• C. 10¹⁷
• D. 10¹⁶

Answer 1

The Correct Option is D

To find the number of photons emitted per second by a monochromatic light source, we first need to determine the energy of a single photon and then find how many such photons constitute the given power output.

Step 1: Calculate the energy of a single photon

The energy \(E\) of a photon can be calculated using the formula:

\(E = \frac{hc}{\lambda}\)

Where:

• \(h = 6.6 \times 10^{-34} \ \text{Js}\) (Planck’s constant)
• \(c = 3 \times 10^{8} \ \text{m/s}\) (speed of light)
• \(\lambda = 600 \ \text{nm} = 600 \times 10^{-9} \ \text{m}\) (wavelength)

Now substituting these values:

\(E = \frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{600 \times 10^{-9}}\)

\(E = \frac{19.8 \times 10^{-26}}{600 \times 10^{-9}}\)

\(E = 3.3 \times 10^{-19} \ \text{J}\)

Step 2: Calculate the number of photons emitted per second

The power \(P\) delivered by the light source is given as \(3.3 \times 10^{-3} \ \text{W}\), which is \(3.3 \times 10^{-3} \ \text{J/s}\). The number of photons \(n\) emitted per second is given by:

\(n = \frac{P}{E}\)

Substituting the values we have:

\(n = \frac{3.3 \times 10^{-3}}{3.3 \times 10^{-19}}\)

\(n = 10^{16}\)

Therefore, the correct answer is \(10^{16}\).

In conclusion, the number of photons emitted per second by the source is 10¹⁶.