Determine the wavelength of the radiation required to excite the electron in `Li^(+ +)` from the first to the third Bohr orbit.

Explanation

If E=hv be the energy absorbed, then
we know, `" " hv=DeltaErArrhv=E_(4)-E_(1)`
Uning the relaion , `E_(n)=(-13.6)/(n^(2))`
For n=4 `" " E_(4)=(-13.6)/(4^(2))`
`=(-13.6)/(16)=-0.85 eV" " ....(i)`
As, H-atom at ground lefvel, for na=1
`[ :. 1 eV=1.6xx10^(-19) J and h=6.62xx10^(-34) J]`
`E_(1)=-13.6 eV " " ....(ii)`
`:.` From Eqs . (i) and (ii) ,we get
`hv=-0.85-(-13.6)`
`=12.75 eV`
`=12.75xx1.6xx10^(-19) J`
`v=(12.75xx1.6xx10^(-19))/(6.62xx10^(-34))=3.8xx10^(15)Hz`
Using the relation , `c=vlambda`,
we get `lambda=(c)/(v)=(3xx10^(8))/(3.8xx10^(15))=974.02xx10^(-10)m~~974Å`