Question

Find number of photons emitted per second by a light source of wavelength \(663\,\text{nm}\) at power \(6\,\text{mW}\). If \(h = 6.63 \times 10^{-34}\,\text{Js}\) is \(N \times 10^{15}\), then find \(N\).

Hint:

Photon count problems are easiest when you remember: {Number of photons per second = Power ÷ Energy of one photon}.

Answer 1

Correct Answer: 20

Concept:
Energy of a single photon is given by: \[ E = \frac{hc}{\lambda} \] Power of the source represents energy emitted per second: \[ P = \frac{\text{Total energy emitted per second}}{\text{time}} \] Hence, number of photons emitted per second: \[ n = \frac{P}{E} \]
Step 1: Convert Given Quantities into SI Units
\[ P = 6\,\text{mW} = 6 \times 10^{-3}\,\text{W} \] \[ \lambda = 663\,\text{nm} = 6.63 \times 10^{-7}\,\text{m} \]
Step 2: Calculate Energy of One Photon
\[ E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34})(3 \times 10^{8})}{6.63 \times 10^{-7}} \] \[ E = 3 \times 10^{-19}\,\text{J} \]
Step 3: Calculate Number of Photons Emitted per Second
\[ n = \frac{6 \times 10^{-3}}{3 \times 10^{-19}} = 2 \times 10^{16} \]
Step 4: Express in Required Form
\[ 2 \times 10^{16} = 20 \times 10^{15} \] \[ \boxed{N = 20} \]