The electron energy in hydrogen atom is given by `E_(n)=-(2.18 xx 10^(-18))/(n^2) J`. Calculate the energy required to remove an electron completely from the n=2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Answer

`5.425xx10^(-12)ergs, 3.7xx10^(-5)cm`

Explanation

`E_(n)=(-21.7xx10^(-12))/(n^(2)) 1 erg =10^(-7)` Joule
`E_(n)=(-21.7xx10^(-12))/(4)`
`J.E.=0-[(-21.7xx10^(-12))/(4)]=(21.7xx10^(-12))/(4)`
`=5.425xx10^(-12)` ergs
(b) `5.425xx10^(-12)=(6.624xx10^(-34)xx10^(8))/(lambda)`
`lambda=(6.624xx3xx10^(8)xx10^(12))/(5.425xx10^(34))=3.7xx10^(-14)(nm)`
`3.7xx10^(-14)xx10^(9)cm=3.7xx10^(-5)cm`