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 ?

1 Answer
Mar 2, 2018

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