Question

A bulb emitted electromagnetic radiation of 660nm wavelength. The total energy of radiation is $3 \times {10^{ - 18}}J$. The number of emitted photon will be:
(A) 1
(B) 10
(C) 100
(D) 1000

Answer 1

Hint: The above question is based on the relation known as Planck-Einstein relation which is the relation between Energy of radiation, Planks’ constant, speed of light and wavelength of light.

Complete answer:
Max Planck and Albert are two important limbs in modern physics. We all know what they did for us. By looking at two different events, they derived a formula applicable to all.
Einstein observed that the energy-momentum relations are different for massive and massless particles. He then came up with a formula for the energy-momentum relation valid for all speed. This formula is known and Einstein's mass energy equivalence$E = m{c^2}$. This formula states that the energy (E) of a particle in its rest frame is given by the product of mass (m) and the speed of light squared. In other words, the mass of a particle at rest is equal to its energy (E) divided by the speed of light squared.
Another great scientist Max Planck saw two different radiation laws for low and high frequencies of radiation. He then derived the radiation law valid for all type’s frequencies. While doing so, he came up with "Planck's'' constant, which is denoted by h. Without this constant, you cannot do quantum mechanics.
The Planck–Einstein relation is a fundamental equation in quantum mechanics which states that the energy of a photon(E) known as photon energy, is proportional to its frequency ν and it is denoted by:
$E = nh\nu $
where h is the planck's constant with a value of $6.6 \times {10^{ - 34}}J$ and n is the number of photons.
Also, we know that the relationship between frequency and wavelength is expressed by the formula-
$\nu = \dfrac{c}{\lambda }$
where c is the speed of light
lambda is the wavelength of radiation, and
v is the frequency
By replacing the value of v in the Planck-Einstein relation, we get
$E = nh\nu = nh\dfrac{c}{\lambda }$
Now, by substituting the values of energy of radiation, Planck’s constant, speed of light and wavelength, we get
$ 3 \times {10^{ - 18}}J = \dfrac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8} \times n}}{{660 \times {{10}^{ - 9}}}} $
$n = \dfrac{{30}}{3} = 10$

Therefore, the correct answer of the given solution is option (B) 10.

Note:
The units given in the question for different values like for energy, wavelength, frequency etc. is very important for finding out the number of photons. You have to be very careful while substituting and be sure to make the conversion for the units (generally in SI units).