[Solved] In a Bohr orbit of hydrogen atom, the ratio of kinetic energ (2023)

Concept:

• Bohrdeveloped theBohr’smodelof theatom, in which he proposed that energy levels ofelectronsare different and the electrons revolve in stable orbits around theatomic nucleus.

According toBohr’s modelrelation between Kinetic energy, potential energy, and total energy of an electron in anatom can be given as:

\(K.E= - TE=\frac{-U}{2}\)-- (1)

Where kinetic energy = K.E

Potential energy = P.E = U

Total energy = K.E + U = T.E

According to the given formula of total energy and kinetic energy of electrons in nth orbit:

Explanation:

From the above concept (eq 1)it is clear that the Potential energy is twice of kinetic energy and negative of it.

So, the required ratio between kinetic energy and potential energy is - 1/2.

Important Points

\(\text{Total }\!\!~\!\!\text{ Energy }\!\!~\!\!\text{ in }\!\!~\!\!\text{ nth }\!\!~\!\!\text{ orbit }\!\!~\!\!\text{ }\left( {{E}_{n~}} \right)=~-13.6~\frac{{{Z}^{2}}}{{{n}^{2}}}eV\)