question_answer

The ionisation potential of hydrogen atom is -13.6 eV. An electron in the ground state of a hydrogen atoms absorbs a photon of energy 12.75 eV. How many different spectral line can one expect when the electron make a downward transition?

A)  1                                            

B)  4

C)  2                                            

D)  6

Correct Answer: D

Solution :

                 \[E={{E}_{1}}/{{n}^{2}}\] Energy used for excitation is 12.75 eV ie, \[(-13.6+12.75)eV=-0.85\,eV\] Energy levels of H-atom The photons of energy 12.75 eV can excite the fourth level of H-atom. Therefore, six lines will be emitted, \[\left( n\left( \frac{(n-1)}{2} \right)\text{lines} \right).\]