Energy from the sun is recived on earth at the rate of `2` cal per `cm^(2)` per min. If avergae wavelength of solar light be taken at `5500 A` then how many photons are recived on the earth per `cm^(2)` per min ?
`(h =6.6 xx 10^(-34)J-s, 1cal = 4.2J)`

Options

A. `1.5 xx 10^(13)`
B. `2.9 xx 10^(13)`
C. `2.3 xx 10^(19)`
D. `1.75 xx 10^(19)`

Answer

C

Explanation

Energy received from the sun
`= 2 cal cm^(-2) (min)^(-1)`
`= 8.4 J cm^(-2) (min)^(-1)`
Energy of `1` photon recived from sun,
`E = (hc)/(lambda) = (6.6 xx 10^(-34) xx 3 xx 10^(8))/(5500 xx 10^(-10))`
`= 3.6 xx 10^(-19) J`
`:.` Number of photos reaching the earth per `cm^(2)` per minute will be
`n = ("energy received from sun")/("energy of one photon")`
or `n = (8.4)/(3.6 xx 10^(-19)) = 2.3 xx 10^(19)`