First slide

Photoelectric effect and study of photoelectric effect

Question

A 60 W bulb is place d at a distance of 4 m from you. The bulb is emitting light of wavelength 600 nm uniformly in all directions. In 0.1 s, how many photons enter your eye if the pupil of the eye is having a diameter of 2 mm? [Take hc = 1240 eV-nm]

Moderate

A

$2.84 \times 10^{12}$
B

$2.84 \times 10^{11}$
C

$9.37 \times 10^{11}$
D

$6.48 \times 10^{11}$

Solution

The intensity of light at the location of your eye is
$I = \frac{P}{4 π r^{2}} = \frac{60}{4 π \times 4^{2}} {Wm}^{- 2}$
The energy entering into your eye per second is
$P_{1} = I \times \frac{π d^{2}}{4}$
where d is the diameter of pupil.
$\begin{matrix} P_{1} = \frac{60}{4 π \times 4^{2}} \times \frac{π \times {(2 \times 10^{- 3})}^{2}}{4} \\ = 9.375 \times 10^{- 7} {Js}^{- 1} \end{matrix}$
Let n be the number of photons entering into the eye per second, then
$\begin{array}{l} P_{1} = n \times \frac{h c}{λ} \\ 9.375 \times 10^{- 7} = n \times \frac{1240 \times 1.6 \times 10^{- 19}}{600} \\ n = 2.84 \times 10^{12} photon s^{- 1} \end{array}$
So, the number of photons entering the eye in 0.1 s= 0.1 n $= 2.84 \times 10^{11}$

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