QJEEM24Phca3d: JEE Main 2024 Physics - Class 12 JEEM24Phca3d Solution: Monochromatic light of frequency is produced by a laser. The…

To find out the number of photons emitted per second by the laser, we can use the relationship between the energy of a single photon, the total energy emitted per second (power), and the number of photons emitted per second. The energy $E$ of a single photon is given by Planck's equation:

$E = hf$

where:

• $h$ is Planck's constant ( $6.63 \times 10^{-34} \mathrm{Js}$ ), and
• $f$ is the frequency of the light ( $6 \times 10^{14} \mathrm{Hz}$ ).

Let's first calculate the energy of one photon:

$E = (6.63 \times 10^{-34} \mathrm{Js}) \times (6 \times 10^{14} \mathrm{Hz})$

$E = 3.978 \times 10^{-19} \mathrm{J}$

The power ( $P$ ) emitted by the laser is the total energy emitted per second,

$P = E_{\text{total per second}} = 2 \times 10^{-3} \mathrm{W} = 2 \times 10^{-3} \mathrm{J/s}$

The number of photons ( $N$ ) emitted per second can be found by dividing the total energy emitted per second by the energy of one photon:

$N = \frac{P}{E}$

Substitute the values we have:

$N = \frac{2 \times 10^{-3} \mathrm{J/s}}{3.978 \times 10^{-19} \mathrm{J}}$

$N = \frac{2 \times 10^{-3}}{3.978 \times 10^{-19}}$

$N = 5.03 \times 10^{15} \text{ photons per second}$

The number of photons emitted per second is approximately $5 \times 10^{15}$ . Therefore, the correct answer, rounded to one significant figure, is:

Option A: $5 \times 10^{15}$