Question

A bulb emits light of wavelength $\lambda =4500A˚$. 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?

Answer 1

Step 1: Given data

1. The wavelength of the light is $\lambda =4500A˚$.
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 $\lambda$ is $E=\frac{hc}{\lambda }$, 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, $P=\frac{E}{t}$.

Step 3: Finding the number of photons

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

Considering $3\times {10}^{8}m/s$ is the velocity of light in free space and $6.626\times {10}^{-34}j.s$ is the Plank constant.

The energy emitted by the bulb is,

$$\begin{gathered} ∆E=150\times \frac{8}{100}=12 \\ ∆E=12joule. \end{gathered}$$

The energy of 1 photon is,

$$\begin{gathered} E=\frac{hc}{\lambda }=\frac{\left(6.626\times {10}^{-34}\right)\times 3\times {10}^8}{4500\times {10}^{-10}}=4.42\times {10}^{-19}joule. \\ orE=4.42\times {10}^{-19}joule. \end{gathered}$$

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

$$\begin{gathered} nE=12joule \\ orn\times 4.42\times {10}^{19}=12. \\ orn=\frac{12}{4.42\times {10}^{-19}}=2.72\times {10}^{19}. \\ orn=2.72\times {10}^{19}. \end{gathered}$$

Therefore, the number of photons emitted by the bulb is $n=2.72\times {10}^{19}.$