At the given point of time, the earth receives energy from sun at `4 cal cm^(-2) mi n^(-1)` .Determine the number of photons received on the surface of the Earth per `cm^(2)` per minute. (Given `:` Mean wavelength of sun light `= 5500 Å` )

Explanation

Given data `:`
Energy received by Earth from sun` E = 4 cal cm^(-2) mi n^(-1)`
To find `:`
No. of photons received by earth from sun n = ?
Planck's constant `h = 6.6 xx 10^(-34) Js`
Mean wavelength of sunlight `lambda = 5000Å`
`E =( n . hc)/( lambda) `
`E = n (( 6.6 xx 10^(-34) xx 3 xx 10^(8))/( 5500 xx 10^(-10)))`
`( E )/( n ) = 3.6 xx 10^(-19) J`
To convert J to cal. `1J = 0.239 cal`
`( E )/(n )= 3.6 xx 10^(-19) xx 0.239 `
`n = ( 4)/( 3.6 xx 10^(-19) xx0.238 ) `
`n = 4.66 xx 10^(19)`