Quantum Mechanics - Laser

The approximate number of photons in a femtosecond (10⁻¹⁵ s) pulse of 600 nanometers wavelength light from a 10-kilowatt peak-power dye laser is

A. 10³
B. 10⁷
C. 10¹¹
D. 10¹⁵
E. 10¹⁸

(GR9677 #59)

Solution:

Number of photon, n = E_total / E_single

Energy of a single photon,  E_single = hc/λ 

h = 6.63 × 10⁻³⁴ Js
c = 3 × 10⁸ m/s
λ  =  600 nanometers = 600 × 10⁻⁹ m

→ E_single = 3 × 10⁻¹⁹  J

From Power, P = W/t = E_total/t

→ Total energy, E_total =  Pt

P = 10 kW = 10⁴ W
t = 10⁻¹⁵ s

→ E_total = 10⁻¹¹ J

n = E_total / E_single = 10⁻¹¹  / (3 × 10⁻¹⁹)  = 0.3 × 10⁸ = 3 × 10⁷  J

Answer: B