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?

Explanation

The energy in the second Bohr orbit
`E_(2)=(21.7xx10^(-19))/((2)^(2))J=-5.44xx10^(-19)J`
For the removal of electron has to be moved to an infinite distance for which `n=oo` and
`E_(oo)=(-2.177xx10^(-18)J)/((oo)^(2))=0`
`DeltaE=E_(oo)-E_(2)=0-(-5.44xx10^(-19)J)`
`=5.44xx10^(-19)J`
=Energy needed to remove the electron from second Bohr orbit of `H` atom
Energy of photon, `E=hv`=Ionisation energy
`:.DeltaE=hv=(hc)/lambda=5.44xx10^(-19)J`
and `lambda=(hc)/(DeltaE)=(6.6xx10^(-34)J sxx3xx10^(8) m s^(-1))/(5.44xx10^(-19)J)`
`=3.64xx10^(-7) m=364xx10^(-9) m=3640 Å`