# What is the number of photons of light with a wavelength

Question.

What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy?

Solution:

Energy $(E)$ of a photon $=h v$

Energy $\left(E_{n}\right)$ of ' $n$ ' photons $=n h v$

$\Rightarrow n=\frac{E_{n} \lambda}{\text { hc }}$

Where, $\lambda=$ wavelength of light $=4000 \mathrm{pm}=4000$

$\times 10^{-12} \mathrm{~m} \mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8}$

$\mathrm{m} / \mathrm{s} \mathrm{h}=$ Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$

Substituting the values in the given expression of $n$ :

$n=\frac{(1) \times\left(4000 \times 10^{-12}\right)}{\left(6.626 \times 10^{-34}\right)\left(3 \times 10^{8}\right)}=2.012 \times 10^{16}$

Hence, the number of photons with a wavelength of 4000 pm and energy of 1 J are

$2.012 \times 10^{16}$