Question

The ionisation potential of hydrogen atom is $ 13.6 \,eV $ . The energy required to remove an electron from the second orbit of hydrogen will be

• A. $ 27.4 \,eV $
• B. $ 13.6 \, eV $
• C. $ 3.4 \, eV $
• D. None of these

Answer 1

Answer: (C)

The potential energy of hydrogen atom
$E_{n}=-\frac{13.6}{n^{2}} eV$
So, the potential energy in second orbit is
$E_{2}=-\frac{13.6}{2^{2}} eV $
$\Rightarrow E_{2}=-\frac{13.6}{4}eV $
$=-3.4\,eV$
Now, the energy required to remove an electron from second orbit to infinity is
$U=E_{\infty}-E_{2}$ [from work-energy theorem and $E_{\infty}=0]$
$\Rightarrow U = 0 − \left(−3.4\right)\, eV $
or $U = 3.4 eV $
Hence, the required energy is $3.4\,eV$.