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 xx10^(13)`
B. `2.9 xx10^(13)`
C. `2.3 xx10^(19)`
D. `1.75 xx10^(19)`

Answer

C

Explanation

Energy received `=2 "cal cm"^(-2) ("min")^(-1)`
`=8.4 " Jcm"^(-2) ("min")^(-1)`
Energy of one photon –
`E=(hc)/lamda=(6.6 xx10^(-34) xx3 xx10^8)/(5500xx10^(-10))=3.6 xx10^(-19)J`
No. of photon = `("Energy received")/("Energy of one photon") `
`=(8.4)/(3.6xx10^(-19))=2.3 xx10^(+19)`