Q36 (2026)
Number of photons of equal energy emitted per second by a $6 \text{ mW}$ laser source operating at $663 \text{ nm}$ is ____.
(Given: $h = 6.63 \times 10^{-34} \text{ J.s}$ and $c = 3 \times 10^{8} \text{ m/s}$)
- $5 \times 10^{16}$
- $5 \times 10^{15}$
- $10 \times 10^{15}$
- $2 \times 10^{16}$
### Related Formula
$$P = n \frac{hc}{\lambda}$$
where:
$P$ = Power of the laser
$n$ = number of photons emitted per second
$h$ = Planck's constant
$c$ = speed of light
$\lambda$ = wavelength
### Step 1: Extract Given Variables
$P = 6 \text{ mW} = 6 \times 10^{-3} \text{ J/s}$
$\lambda = 663 \text{ nm} = 663 \times 10^{-9} \text{ m}$
$h = 6.63 \times 10^{-34} \text{ J.s}$
$c = 3 \times 10^8 \text{ m/s}$
### Step 2: Substitution and Calculation
$$6 \times 10^{-3} = \frac{n \times 6.63 \times 10^{-34} \times 3 \times 10^8}{663 \times 10^{-9}}$$
Notice that $6.63 / 663 = 10^{-2}$.
$$6 \times 10^{-3} = \frac{n \times 3 \times 10^{-26} \times 10^{-2}}{10^{-9}}$$
$$6 \times 10^{-3} = n \times 3 \times 10^{-19}$$
$$n = \frac{6 \times 10^{-3}}{3 \times 10^{-19}} = 2 \times 10^{16}$$
### Pattern Recognition
Always look for complementary numerical values like $663$ and $6.63$. It guarantees a clean power of 10 extraction.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Dual Nature of Radiation and Matter
