Question

The ratio of the potential energy to the kinetic energy of an electron in n^th orbit of Bohr model of hydrogen atom is ______.

Options

• `-1/2`

• `1/2`

• 2

• −2

Answer 1

The ratio of the potential energy to the kinetic energy of an electron in n^th orbit of Bohr model of hydrogen atom is −2.

Explanation:

In the Bohr model of a hydrogen atom, the relationship between the energies of an electron in any given orbit is governed by electrostatic forces. For an electron in the n^th orbit, the following energy relationships apply:

The potential energy is given by:

PE = `-(k Z e^2)/r`

It is always negative for a bound electron.

The kinetic energy is given by:

KE = `(k Z e^2)/(2 r)`

It is always positive.

The total energy is the sum of both,

E = PE + KE

= `-(k Z e^2)/r + (k Z e^2)/(2 r)`

= `-(k Z e^2)/(2 r)`

From these formulas, we can derive the ratio:

`(PE)/(KE) = (-(k Z e^2)/r)/((k Z e^2)/(2 r))`

= −2