Question

An electron in hydrogen atom (ground state) jump to higher energy level $x$, such that potential energy of electron becomes half of its total energy at ground state . What is the value of $x$?

Answer 1

• In stationary orbit, $\text{Total energy}=\frac{\text{Potential energy}}{2}$
  
• Energy of electron in ground state of H-atom $=-13.6eV$
• Total energy in $x$ excited state $=\frac{-13.6}{x^2}eV$
• Potential energy in $x$ excited state $=\frac{-13.6\times 2}{x^2}eV$
  
• According to the question, potential energy in excited state $=\frac{-13.6}{2}eV$
• Therefore, $\frac{-13.6}{2}=\frac{-13.6\times 2}{x^2}$

$x=\sqrt{4}=2$