Question

A point source of light of power $P$ and wavelength $\lambda$ is emitting light in all directions. The number of photons present in a spherical region of radius $r$ to radius $r+x$ with centre at the source is:

• A. $\frac{P\lambda }{4\pi r^{2}hc}$
• B. $\frac{P\lambda x}{h{c}^2}$
• C. $\frac{P\lambda x}{4\pi r^{2}hc}$
• D. None of these

Answer 1

The correct option is B $\frac{P\lambda x}{h{c}^2}$

The energy stored in the spherical region between $r$ and $r+x$ is

= energy density$\times 4\pi r^{2}x=\frac{I}{C}\times 4\pi r^{2}x=\frac{P}{4\pi r^{2}c}4\pi r^{2}x=\frac{Px}{c}$

$\therefore$ Number of photons is the given volume is $=\frac{Px}{h\nu c}=\frac{P\lambda x}{h{c}^2}$