A 60 W bulb is placed at a distance of 4 m from you. The bulb is emtting 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 2mm? [take `hc=1240eV-nm]`

Options

A. `2.84xx10^(12)`
B. `2.84xx10^(11)`
C. `9.37xx10^(11)`
D. `6.48xx10^(11)`

Answer

B

Explanation

The intensity of light at the lacation of your eye is
`I=(P)/(4pir^2)=(60)(4pixx4^2)Wm^(-2)`
The energy entering into your eye per second is
`P_1Ixx(pid^2)/(4)`
where d is the diameter of pupil.
`P_1=(60)/(4pixx4^2)xx(pixx(2xx10^(-3))^2)/(4)`
`=9.375xx10^(-7) Js^(-1)`
Let n be the number of photons enetering into the eye per second , then
`P_1nxx(hc)/(lamda)`
`9.375xx10^(-7)=nxx(1240xx1.6xx10^(-19))/(600)`
`n=2.84xx10^(12)` photon `s^(-1)`
So, the number of photons entering the eye in `0.1 s=0.1n=2.84xx10^(11)`