Question

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

• A. $9 \times 10^{18}$
• B. $6 \times 10^{15}$
• C. $5 \times 10^{15}$
• D. $7 \times 10^{16}$

Answer 1

Answer: (C)

$5 \times 10^{15}$

Answer 2

Given: - Frequency of light: $\nu = 6 \times 10^{14} \, \text{Hz}$ - Power emitted by the source: $P = 2 \times 10^{-3} \, \text{W}$ - Planck's constant: $h = 6.63 \times 10^{-34} \, \text{Js}$

Step 1: Calculating the Energy of One Photon

The energy $E$ of a photon is given by:

$E = h\nu$

Substituting the given values:

$E = 6.63 \times 10^{-34} \times 6 \times 10^{14} \, \text{J}$ $E = 3.978 \times 10^{-19} \, \text{J}$

Rounding off:

$E \approx 4 \times 10^{-19} \, \text{J}$

Step 2: Calculating the Number of Photons Emitted per Second

The number of photons emitted per second ($n$) is given by:

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

Substituting the given values:

$n = \frac{2 \times 10^{-3}}{4 \times 10^{-19}}$ $n = \frac{2}{4} \times 10^{16}$ $n = 0.5 \times 10^{16}$ $n = 5 \times 10^{15}$

Conclusion: The number of photons emitted per second by the source is $5 \times 10^{15}$.