Question

How many photons of a radiation of wavelength $\lambda =5\times 10^{-7}m$ must fall per second on a blackened plate in order to produce a force of $6.62\times 10^{-5}N$ ?

• A. $3\times 10^{19}$
• B. $5\times 10^{22}$
• C. $2\times 10^{22}$
• D. $1.67\times 10^{18}$

Answer 1

Answer: (B)

The momentum of photon $=h/\lambda$
If $n$ is the number of photons falling per second on the plate, then total momentum per second of the incident photons is
$p=n\times \frac{h}{\lambda }$
Since the plate is blackened, all photons are absorbed by it.
$\frac{\Delta p}{\Delta t}=n\frac{h}{\lambda }$
Since $F=\frac{\Delta p}{\Delta t}=n\frac{h}{\lambda }$
$\therefore n=\frac{F\lambda }{h}=\frac{6.62\times 10^{-5}\times 5\times 10^{-7}}{6.62\times 10^{-34}}$
$=5\times 10^{22}$