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 $h = \dfrac{c}{\lambda }$
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
\[E = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{400 \times {{10}^{ - 9}}}} \\
  E = 4.969 \times {10^{ - 19}}J \\
\]
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 $3 \times {10^8}m/s$ 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.