Question

Number of photons of equal energy emitted per second by a 6 mW laser source
operating at wavelength 663 nm is _______.

(Given: h = 6.63 × 10^-34 J·s and c = 3 × 10^8 m/s)

• A. \(10\times10^{15}\)
• B. \(5\times10^{16}\)
• C. \(5\times10^{15}\)
• D. \(2\times10^{16}\)

Hint:

To find photon count, divide laser power by energy of a single photon.

Answer 1

The Correct Option is D

To determine the number of photons emitted per second by a laser source, we start with the basic relationship between energy, wavelength, and power of the source. The power (P) of the laser is given as 6 mW, which can be converted to watts:

\(P = 6 \, \text{mW} = 6 \times 10^{-3} \, \text{W}\)

The energy of each photon can be calculated using the formula:

\(E = \frac{hc}{\lambda}\)

where:

• \(h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\) (Planck's constant)
• \(c = 3 \times 10^{8} \, \text{m/s}\) (speed of light)
• \(\lambda = 663 \, \text{nm} = 663 \times 10^{-9} \, \text{m}\) (wavelength)

Substitute these values into the energy formula:

\(E = \frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{663 \times 10^{-9}} \, \text{J}\)

Calculate the energy of one photon:

\(E = \frac{19.89 \times 10^{-26}}{663 \times 10^{-9}} \approx 2.998 \times 10^{-19} \, \text{J}\)

Now, using the power value, we calculate the number of photons emitted per second:

\(n = \frac{P}{E} = \frac{6 \times 10^{-3}}{2.998 \times 10^{-19}}\)

Calculate the number of photons:

\(n \approx \frac{6 \times 10^{-3}}{2.998 \times 10^{-19}} = 2 \times 10^{16}\)

Therefore, the number of photons emitted per second by the laser source is \(2 \times 10^{16}\).

The correct option is \(2 \times 10^{16}\).