Question

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is?
A- 2: -1
B- 1:1
C- 1: -2
D- 1: -1

Answer 1

Hint: Bohr orbit refers to the orbit in which the electron revolves around the nucleus of the hydrogen atom. That orbit is considered to be circular for easy calculations although the orbit is elliptical in shape. The orbit is a stationary orbit.

Complete step by step answer:
A good analogy of movement of electrons around the nucleus in orbit is the movement of satellites around the earth. The total energy is negative and that is why the satellite/electrons remain bound in the circular orbit.
The relation between kinetic energy, Potential energy, and Total energy for the electron is given as
-TE=KE=-PE/2------(1)
Here TE represents total energy, KE represents kinetic energy and PE represents potential energy.
So, from equation (1) the ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom,
\[\dfrac{KE}{TE}=1:-1\]

So, the correct answer is “Option D”.

Additional Information:
The Bohr model states that electrons in atoms move in circular orbits around the nucleus and they do so in certain fixed circular orbits at a discrete set of distances from the nucleus. In these orbits they do not radiate energy.

Note:
In moving in these stationary orbits they can jump to higher orbits by absorbing energy and can jump back to lower orbits by emission of energy. Planck radiation formula gives the relationship between the energy absorbed.