Question

A ruby laser delivers a 10 ns pulse of 1 MW average power. If all the photons are of the same wavelength 694.3 nm, how many photons are contained in the pulse?
1. 3.5 × 10¹⁶
2. 6.2 × 10¹⁶
3. 2.6 × 10¹⁵
4. 4.0 × 10¹⁴

Answer 1

Correct Answer - Option 1 : 3.5 × 10¹⁶

Concept:

Light contains energy in discrete packets (or particles) called photons. The amount of energy in those photons is calculated by this equation:

E = hν

E is the energy of the photon in Joules

h is Planck's constant (6.63 × 10^-34 Js)

ν (Hz) is the frequency of the light

Calculation:

From the pulse width and average power, we can find the energy delivered by each pulse. The number of photons can then be found by dividing the pulse energy by the energy of each photon, which is determined from the photon wavelength.

The energy in each pulse is:

E = P × t = 1 × 10⁶ × 10 × 10^-9

E = 0.01 J

The energy of each photon:

\({E_\gamma } = h\nu = \frac{{hc}}{\lambda } = \frac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{694.3 \times {{10}^{ - 9}}}} \)

\(E= 2.86 \times {10^{ - 19}}\;J\)

\(N = \frac{E}{{{E_\gamma }}} = \frac{{0.01}}{{2.86 \times {{10}^{ - 19}}}} \)

\(N= 3.5 \times {10^{16}}\;photons\)