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Question: A 100 watt bulb emits monochromatic light of wavelength 400nm. Calculate the number of photons emitt...

A 100 watt bulb emits monochromatic light of wavelength 400nm. Calculate the number of photons emitted per second by the bulb.
(A) 3×1020s−13 \times {10^{20}}{s^{ - 1}}
(B) 2×10−20s−12 \times {10^{ - 20}}{s^{ - 1}}
(C) 2×1020s−12 \times {10^{20}}{s^{ - 1}}
(D) 1×10−20s−11 \times {10^{ - 20}}{s^{ - 1}}

Explanation

Solution

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=cλh = \dfrac{c}{\lambda }
Where h=6.626×10−34Js,c=3×108ms−1h = 6.626 \times {10^{ - 34}}Js,c = 3 \times {10^8}m{s^{ - 1}}
Also the wavelength λ=400nm=400×10−9m\lambda = 400nm = 400 \times {10^{ - 9}}m
Now we substitute these values in the equation E = hv

E=4.969×10−19J  E = 4.969 \times {10^{ - 19}}J \\\

Now, the number of photons can be calculated as
Power = energy of one photon ×\times number of photons emitted per sec
n \times 4.969 \times {10^{ - 19}} = 100 \\\ n = \dfrac{{100}}{{4.969 \times {{10}^{ - 19}}}} \\\ n = 2.012 \times {10^{20}} \\\

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 3×108m/s3 \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=λf.c = \lambda f.
By substituting the values of the parameters in the above equation, energy of a photon can be calculated.