Question

How much energy is required to excite an electron in the ground state in a hydrogen atom to the third excited state? How much more energy would it take to ionise the atom ?

Answer 1

Energy required is 12.75 eV
and 0.85 eV more to ionise the atom

Explanation:

According to Bohr's model of H atom ,
the Energy of electron in the n-th shell is given by ,

`E_n = -13.6/n^2 eV`

Energy required to excite from initial state to final state

`E = E_f - E_i` , where `E_f` and `E_i` are final and initial energy states

Remember this always, the count of states start from one. So ground state is n=1 , first excited state is n=2 , second is n=3 ...etc.

So ,`E = - 13.6/(4)^2 - (-13.6/(1)^2) = 12.75 eV` .
ionising an atom means exciting the electron to the infinite excited state , so that it is no longer attached to the atom. This leaves a positive ion behind.

`E = -13.6/oo^2 - (-13.6/(4)^2) = 0.85 eV`

So you need 0.85 eV more than 12.75 eV to ionise the atom