Question

Assume that a 100 W sodium vapour lamp rediates its energy uniformly in all directions in the form of photons with an associated wavelength of 589 nm.
At what distance from the lamp will the average flux of photons be 1.00 photons /$\left(c{m}^{2}s\right)$ ?

Answer 1

Energy of single photon is given as,

$E=\frac{hc}{\lambda }$

Let $N$ be the number of photons emitting per second.

Thus, power $P=\frac{Nhc}{\lambda }⟹N=\frac{P\lambda }{hc}$

Thus, at distance $d$ from the light source, the average flux of photons will be, $\frac{P\lambda }{hc\times 4\pi d^2}$

So, $\frac{100\times 589\times {10}^{-9}}{6.63\times {10}^{-34}\times 3\times {10}^8\times 4\pi \times d^2}=1.00photons/\left(c{m}^{2}s\right)⟹d=4.85\times {10}^{9}cm$