AIPMT 2010 Physics and Chemistry Paper

Energy of an hydrogen like atom like He+in an n‌th ‌ orbit is given by
En=−‌

13.6Z2

n2

‌eV
For hydrogen atom, Z=1
∴‌‌En=−‌

13.6

n2

‌eV
For ground state, n=1
∴‌‌E1=−‌

13.6

12

‌eV=−13.6‌eV
For He+ion, Z=2
En=−‌

4(13.6)

(2)2

‌eV=−13.6‌eV
For first excited state, n=2
∴‌‌E2=−‌

4(13.6)

(2)2

‌eV=−13.6‌eV
Hence, the energy in He+ion in first excited state is same that of energy of the hydrogen atom in ground state i.e., −13.6‌eV