The total energy (sum of kinetic and electrostatic potential) of

SOLUTION

CONCEPT:

• Potential energy: An electron possesses some potential energy because it is found in the field of nucleus potential energy of an electron in nth orbit of radius rn is given by

\(U = - \frac{{{e^2}}}{{4\pi {\epsilon_0}r}}\)

Where r = radius and e = charge on the electron

• Kinetic energy: Electron possesses kinetic energy because of its motion. 
• Closer orbits have greater kinetic energy than outer ones.

\(K =\frac{{{e^2}}}{{8\pi {\epsilon_0}r}} \)

EXPLANATION:

• Total energy: Total energy (TE) is the sum of potential energy and kinetic energy i.e.

⇒ E = K + U

\(\Rightarrow E=\frac{{{e^2}}}{{8\pi {\epsilon_0}r}} - \frac{{{e^2}}}{{4\pi {\epsilon_0}r}} = \; - \frac{{{e^2}}}{{8\pi {\epsilon_0}r}}\)

• Therefore, the total energy of electron in orbit of the hydrogen atom is negative.
• Hence, the electron is bound to the nucleus, i.e., the electron is not free to leave the orbit around the nucleus.