The electron energy in hydrogen atom is given by `E=(-21.7 xx 10^(-12))ln^2` ergs. Calculate the energy required to remove an electron completely from the n=2 orbit. What is the longest wavelength in cm of light that can be used to cause this transition?

Explanation

The photon capable of removing an electron from the first bohr orbit posses energy `= 13.6eV`
`= 13.6 xx 1.602 xx 10^(-19) J`
`= 21.787 xx 10^(-19) J`
`," E = (hc)/(lambda)`
`21.787 xx 10^(-19) = (6.625 xx 10^(-34) xx 3.0 xx 10^(8))/(lambda)`
`:. lambda = 912.24 xx 10^(-10)m = 912.24 Å`
Energy of photon `E = Nhv = (Nhv)/(lambda)`
:. Number of photon electrons emitted per minut
`(N) = (E lambda)/(hc)`
`= (6000 J xx 300 xx 10^(-9)m)/(6.626 xx 10^(-34) J s xx 3 xx 10^(8) ms^(-1))`
`= 9.05 xx 10^(22)`photons