How many photons are received on earth per `cm^-2` per hour if the energy from the sun reaching on the earth is at the rate of `2cal cm^(-2) min^(-1)` and average wavelength of solar light be taken as 5500Å. Use `h=6.6xx10^(-34)J , c=3xx10^8ms^(-1)` and `1cal =4,2J`

Explanation

Here, `lambda=5500Å =5500xx10^(-10)m`
Rate of solar energy reaching earth from the sun
`=2calcm^-2min^-1=2xx4.2Jcm^-2min^-1`
`=2xx4.2xx60Jcm^-2hour^-1`
Energy of photon received on earth
`E=(hc)/lambda=((6.6xx10^(-34))xx(3xx10^8))/(5500xx10^(-10))`
`=3.6xx10^(-19)J`
If n number of photons is reaching the earth per `cm^2`per hour, then total energy will be
`=nE=nxx3.6xx10^(-19)J cm^-2h^-1`
`:. nxx3.6xx10^(-19)=2xx4.2xx60`
or `n=(2xx4.2xx60)/(3.6xx10^(-19))=1.4xx10^(21)`