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A sensor is exposed for 0.1 s to a 200 W...

A sensor is exposed for 0.1 s to a 200 W lamp 10m away The sensor has an opening that is 20 mm in diameter. How many photons enter the sensor if the wavelength of light is 600nm? Assume that all the energy of the lamp is given off as light.

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Energy of photon,
`E=(hc)/(lamda)=(6.62xx10^-34xx3xx10^8)/(600xx10^-9)approx3.3xx10^-19J`
The number of photons emitted per second,
`n=(200)/(3.3xx10^-19)=6.1xx10^20s^-1`
The radiation is spherically symmetrical, the number of photons entering the sensor per second is the product of n and ratio of aperture area to the area of sphere of radius 10m:
`(6.1xx10^20)(lamdaxx(0.01)^2)/(4xxpixx10^2)=1.53xx10^14` `photons s^-1`
Therefore, number of photns entering the sinsor in 1 `s=(0.1)xx(1.53xx10^14)=1.53xx10^13`.
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