Question

A sodium incandescent bulb emits $589nm$ wavelength light at $60watts$. calculate the number of photons emitted by the bulb.

Answer 1

Step1: Given data

1. The wavelength of the sodium incandescent bulb light is $\lambda =589\times {10}^{-9}m.$
2. The total energy of the light is $E=60watt.$
3. The energy of each photon of wavelength $\lambda$ is defined by the form $E=\frac{hc}{\lambda }$, where, h is the Plank constant and c is the velocity of light in free space.

Step 2: Finding the number of photons

Let there be n number of photons exist in the $60watt$ light.

The energy of one photon is $E=\frac{hc}{\lambda }$.

So,

$$\begin{gathered} E=\frac{hc}{\lambda }=\frac{\left(6.626\times {10}^{-34}\right)\times \left(3\times {10}^8\right)m/s^{-1}}{589\times {10}^{-8}m}=3.37\times {10}^{-20}\because \left(c=speedoflight=3\times {10}^{8}m/s^{-1}\right) \\ orE=3.37\times {10}^{-20}watt. \end{gathered}$$

So, the number of photons is

$$\begin{gathered} n=\frac{Totalenergyoflightsource}{Energyofeachphoton}=\frac{60}{3.37\times {10}^{-20}}=1.7\times {10}^{21} \\ orn=1.7\times {10}^{21} \end{gathered}$$

Therefore, the number of photons emitted by the bulb is $1.7\times {10}^{21}$.