Question

The number of photons falling per second on a completely darkened plate to produce a force of $6.62\times 10^{-5} \, N$ is $n$ . If the wavelength of the light falling is $5\times 10^{- 7} \, m,$ then $n=\ldots \times 10^{22} \cdot\left(h=6.62 \times 10^{-34} J - s \right)$

• A. $1$
• B. $5$
• C. $0.2$
• D. $3.3$

Answer 1

Answer: (B)

Energy carried by $n$ photons per second
$P=n.\frac{h c}{\lambda }$
As photons get absorbed by dark plate, force experienced by the plate
$F = \frac{1}{C} . \, n \frac{h e}{\lambda }$
Or $F\times c=n.\frac{h c}{\lambda }$ $\left[a s \, p o w e r \, \left(P\right) = f o r c e \times s p e e d\right]$
$=F\times c$
Or $n=\frac{F \lambda }{h}=\frac{6.62 \times 10^{- 5} \times 5 \times 10^{- 7}}{6.62 \times 10^{- 34}}=5\times 10^{22}$