Question

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

• A. $27.4eV$
• B. $13.6eV$
• C. $3.4eV$
• 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
$E_2=-\frac{13.6}{2^2}eV$
$\Rightarrow E_2=-\frac{13.6}{4}eV$
$=-3.4eV$
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 $U=3.4eV$
Hence, the required energy is $3.4eV$.