Question

A 100 watt bulb emits monochromatic light of wavelength 400nm. Calculate the number of photons emitted per second by the bulb.
(A) $3\times {10}^{20}{s}^{-1}$
(B) $2\times {10}^{-20}{s}^{-1}$
(C) $2\times {10}^{20}{s}^{-1}$
(D) $1\times {10}^{-20}{s}^{-1}$

Answer 1

Hint- Before calculating the number of photons emitted per second by the bulb we would collect the data given in the question and we will use a formula of energy of photon to calculate the energy of a single photon and then we will find the number of photons in 100watt of energy.

Complete step by step solution:
Given ;Power of the bulb = 100watt
Energy of one photon is E = hv
As we know $h={\displaystyle \frac{c}{\lambda }}$
Where $$h=6.626\times {10}^{-34}Js,c=3\times {10}^{8}m{s}^{-1}$$
Also the wavelength $\lambda =400nm=400\times {10}^{-9}m$
Now we substitute these values in the equation E = hv
$$\begin{gathered} E={\displaystyle \frac{6.626\times {10}^{-34}\times 3\times {10}^8}{400\times {10}^{-9}}} \\ E=4.969\times {10}^{-19}J \end{gathered}$$
Now, the number of photons can be calculated as
Power = energy of one photon $\times$ number of photons emitted per sec
$$\begin{gathered} n\times 4.969\times {10}^{-19}=100 \\ n={\displaystyle \frac{100}{4.969\times {10}^{-19}}} \\ n=2.012\times {10}^{20} \end{gathered}$$

Hence, the correct option is C.

Additional Information- A photon is the smallest amount of discrete electromagnetic radiation, or quantity. It is the fundamental unit of all light. Photons are always in motion and travel at constant speed in a vacuum to all $3\times {10}^{8}m/s$ observers. This is commonly referred to as light speed, as the letter c denotes it. According to Einstein's light quantum theory, photons have energy equal to Planck 's constant of their oscillation frequency times. Einstein proved that light is a photon flow, the energy of these photons is the height of their oscillation frequency and the light intensity corresponds to the photon number.

Note- To solve these types of questions, we need to calculate the energy of photons which is calculated by using the formula mentioned above and also by the formula E = hf where E is the energy, h is the planck's constant and f is the frequency of the photon in Hz. Also the relation between speed of light and frequency is given by $c=\lambda f.$
 By substituting the values of the parameters in the above equation, energy of a photon can be calculated.