Question 94: Dual Nature of Matter and Radiation

Question

Monochromatic light of frequency $6 	imes 10^{14} \mathrm{~Hz}$ is produced by a laser. The power emitted is $2 	imes 10^{-3} \mathrm{~W}$. How many photons per second on an average, are emitted by the source ?
(Given $\mathrm{h}=6.63 	imes 10^{-34} \mathrm{Js}$ )

Accepted Answer

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 	imes 10^{-34} \mathrm{Js} $), and
$ f $ is the frequency of the light ($ 6 	imes 10^{14} \mathrm{Hz} $).
Let's first calculate the energy of one photon:
$$ E = (6.63 	imes 10^{-34} \mathrm{Js}) 	imes (6 	imes 10^{14} \mathrm{Hz}) $$
$$ E = 3.978 	imes 10^{-19} \mathrm{J} $$
The power ($ P $) emitted by the laser is the total energy emitted per second,
$$ P = E_{	ext{total per second}} = 2 	imes 10^{-3} \mathrm{W} = 2 	imes 10^{-3} \mathrm{J/s} $$
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:
$$ N = \frac{2 	imes 10^{-3} \mathrm{J/s}}{3.978 	imes 10^{-19} \mathrm{J}} $$
$$ N = \frac{2 	imes 10^{-3}}{3.978 	imes 10^{-19}} $$
$$ N = 5.03 	imes 10^{15} 	ext{ photons per second} $$
The number of photons emitted per second is approximately $5 	imes 10^{15}$. Therefore, the correct answer, rounded to one significant figure, is:
Option A: $5 	imes 10^{15}$

Answer

$5 	imes 10^{15}$

Answer

$7 	imes 10^{16}$

Answer

$6 	imes 10^{15}$

Answer

$9 	imes 10^{18}$

Dual Nature of Matter and Radiation

Monochromatic light of frequency 6 \times 10^{14} \mathrm{~Hz} is produced by a laser. The power emitted is 2 \times 10^{-3} \mathrm{~W}. How many photons per second on an average, are emitted by the source ? (Given \mathrm{h}=6.63 \times 10^{-34} \mathrm{Js} )

Choose the correct answer: