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Question

A bulb emits light of wavelength λ=4500A˚. The bulb is rated as 150watt and 8% of the energy is emitted as light. How many photons are emitted by the bulb per second?


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Solution

Step 1: Given data

  1. The wavelength of the light is λ=4500A˚.
  2. The power of the light is P=150watt.
  3. The energy emitted by the light is 8%.

Step 2: Concept and formulae

  1. The energy of a photon of wavelength λ is E=hcλ, where, h is the Plank constant and c is the velocity of light in free space.
  2. Power is the total amount of energy emitted in a unit of time, P=Et.

Step 3: Finding the number of photons

Let n number of photons being emitted per second by the bulb.

Considering 3×108m/s is the velocity of light in free space and 6.626×10-34j.s is the Plank constant.

The energy emitted by the bulb is,

E=150×8100=12E=12joule.

The energy of 1 photon is,

E=hcλ=6.626×10-34×3×1084500×10-10=4.42×10-19joule.orE=4.42×10-19joule.

According to question light(photon) energy = 12 joule,

nE=12jouleorn×4.42×1019=12.orn=124.42×10-19=2.72×1019.orn=2.72×1019.

Therefore, the number of photons emitted by the bulb is n=2.72×1019.


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