Question

If a 200 watt monochromatic light source emits 4 × 1020 photons per sec, then the wavelength of the light will be -
1. 200 mm
2. 600 mm
3. 400 mm
4. 500 mm

Answer 1

Correct Answer - Option 3 : 400 mm

Calculation:

We know that power = Rate of consumption of energy

The energy of a photon  E = h c / λ 

If  4 × 1020 photon is emitted per second

then total energy consumed in 1 second or power is 

P  = 4 × 1020 E

Given, power is 200 Watt

200 = 4 × 1020 E

\(\implies 200 = 4 \times 10 ^{20} \frac{hc}{λ }\)

Putting values of Planck's constant h, and velocity of light c

'\(\implies 200 = 4 \times 10 ^{20} \frac{(6.626 \times 10 ^{-34})(3 \times 10 ^8)}{λ }\)

⇒ λ = 400 mm

So, the correct option is 400 nm.