# Energy Level - Principle Energy Level

## Bohr’s Atomic Model:

• Thomson’s and Rutherford’s atomic models failed to answer many questions related to the energy of an atom and its stability. In the year 1913, Niels Bohr proposed an atomic model, describing an atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the positively charged nucleus, similar to the planets around the sun in our solar system, with attraction provided by the electrostatic forces.
• This model is popularly known as Bohr model of an atom. Bohr proposed an atomic model of a hydrogen atom.
• Bohr’s model gave a proper explanation for the stability of electrons revolving in orbits. He named these orbits as energy shells. His postulates explaining the energy level are discussed below.

### Bohr’s Explanation for Energy Level:

• Different orbits in which electrons revolve are known as stationary states or energy level. These stationary states/ energy level for an electron are numbered as n = 1, 2, 3……….. These integers are also known as the principal quantum numbers.
• Energy of the stationary state in which an electron is placed is given by:
$\({{E}_{n} = {-R}_{h} \frac{1}{{n}^{2}}}$ \(

Where, RH is called Rydberg constant whose value is 2.18×10–18 J.

• Energy of electron when it is far away from the influence of nucleus is taken as zero. Principal quantum number of an electron existing in such a stationary state is taken as, n = ∞. Such kind of hydrogen atom is called as ionized hydrogen atom. A negative sign is placed in the above equation as, due to the transition of electron from one orbit to another, the stationary state energy is emitted and thus, energy is lowered.
• When an electron is placed in the lowest stationary state/ energy level possible, it is said to be in the ground state. Electron in this energy level revolves in the orbit having smallest possible radii. The energy of this state is –13.6 eV.

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#### Practise This Question

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is