Question

3.a laser beam with an optical power of 5mw has a wavelength of 632.8 nm. calculate the number of photons emitted per second.

Answer 1

1st let us calculate the energy of one photon which has a wavelength of 632.8 nm.

we know that energy of a radiation or photon is given by : E = hc/λ

where h is the planks constant and is equal to 6.625 × 10⁻³⁴ J-sec and given the wavelength of beam = 632.8 × 10⁻⁹ m

substituting in the energy equation we get :

E = (6.625 × 10⁻³⁴ J-sec × 3 × 10⁸ m)/(632.8 × 10⁻⁹ m)

⇒ E = 3.14 × 10⁻¹⁹ Joules.

⇒ The energy of one photon which has wavelength 632.8 nm is 3.14 × 10⁻¹⁹Joules.

given the power of laser beam as 5 MW = 5 × 10⁶ watts =  5 × 10⁶ J/sec

(as we know that 1 watt = 1 joule per second)

⇒ the laser beam emits 5 × 10⁶Joules in one second.

but we know that energy of one photon is 3.14 × 10⁻¹⁹ Joules.

⇒ if energy of one photon is 3.14 × 10⁻¹⁹ Joules then 5 × 10⁶ joules contains how many photons is what we need to calculate.

⇒ Number of photons which make up an energy of 5 × 10⁶  joules is :

= (5 × 10⁶ joules × 1 photon)/(3.14 × 10⁻¹⁹ Joules)

⇒ 1.592 × 10²⁵ photons

⇒ The laser beam of 5 MW power which operates at a wavelength of 632.8 nm emits 1.592 × 10²⁵ photons per second.