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

The Correct Option is C

To find out how many photons are emitted per second by the laser, we need to calculate the energy of a single photon and then determine how many such photons correspond to the total power emitted.

The energy \(E\) of a single photon can be determined using Planck's equation:

\(E = h \times f\)

Where:

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

Substituting the given values into the formula:

\(E = 6.63 \times 10^{-34} \times 6 \times 10^{14}\)

\(E = 3.978 \times 10^{-19} \, \text{J}\)

This is the energy of one photon. The total power \(P\) emitted by the laser is \(2 \times 10^{-3} \, \text{W}\) (which is joules per second).

We can find the number of photons emitted per second by dividing the total power by the energy of a single photon:

\(n = \frac{P}{E} = \frac{2 \times 10^{-3}}{3.978 \times 10^{-19}}\)

Calculating this, we find:

\(n \approx 5.03 \times 10^{15}\)

Therefore, the number of photons emitted per second is approximately \(5 \times 10^{15}\).

Thus, the correct answer is \(5 \times 10^{15}\), which matches with one of the given options.

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 \( 5 \times 10^{15} \).