Question

The number of photons $(\lambda =6630\stackrel{o}{A})$ that strike per second on a totally reflecting screen (as shown in figure), so that a force of $1N$ is exerted on the screen, is approximately:

• A. ${10}^{23}$
• B. ${10}^{27}$
• C. ${10}^{25}$
• D. ${10}^{26}$

Answer 1

Answer: (A)

For each photon, impulse of hitting the surface is given by:

$J=2p\sin \left({30}^o\right)=p$

Let the number of photons hitting the surface in a second be $n$.

Then, net force applied by the photon beam is:

$F=\int nJdt=np$

From debroglie equation,

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

Hence, for force of $1N$,

$1=\frac{n\times 6.63\times {10}^{-34}}{6630\times {10}^{-10}}$

$n={10}^{27}$