First slide

Electromagnetic radiation - Dual nature of radiation and matter

Question

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

Moderate

A

$3 \times 10^{19}$
B

$5 \times 10^{22}$
C

$2 \times 10^{22}$
D

$1.67 \times 10^{18}$

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App