Question.
What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy?
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
$2.012 \times 10^{16}$
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
$2.012 \times 10^{16}$