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

The correct option is B $5\times {10}^{22}$

Momentum of photon is given by,

$p=\frac{h}{\lambda }$

Momentum of n photons, $=n\frac{h}{\lambda }$

Force is the change in momentum. Since, the plate is blackened, all the photons are being absorbed. Thus, change in momentum and hence the force is given by

$F=\frac{dp}{dt}=n\frac{h}{\lambda }$

$n=F\frac{\lambda }{h}=\frac{6.62\times {10}^{-5}\times 5\times {10}^{-7}}{6.62\times {10}^{-34}}=5\times {10}^{22}$