If PE represents potential energy and TE represents the total energy in Bohr's model of the hydrogen atom. Then what will be the effect on PE and TE if an electron goes to a higher level

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 r_n is given by

\(U = - \frac{{kZ{e^2}}}{{{r_n}}}\)

Where Z = atomic number, n = orbit number and r_n = radius of the nth orbit

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

\(K = \frac{{kZ{e^2}}}{{2{r_n}}} =- \frac{U}{2} = \frac{{kZ{e^2}}}{{{2r_n}}}\)

• Total energy: Total energy (TE) is the sum of potential energy and kinetic energy i.e. E = K + U

\(TE = - 13.6\frac{{{Z^2}}}{{{n^2}}}eV\)

The relationship between PE, TE, and KE is given by:

KE = - TE = - PE/2

EXPLANATION:

• From above it is clear that as n increases, the potential energy increases, kinetic energy decreases and total energy increases.
• Therefore, if an electron goes to a higher level, then PE and TE increases.