Atomic Structure

Bohr’s Model of Hydrogen Atom

The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits and are arranged concentrically around the nucleus.

The energy of an electron in the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when it absorbs required amount of energy and its contrary is also true.

The frequency of radiation absorbed or emitted is given by

`ν=(ΔE)/h=(E_2-E_1)/h`

Where, E₁ and E₂ are the energies of the lower and higher allowed energy states. This expression is commonly known as Bohr’s frequency rule.

The agnular momentum of an electron is quantised. For a given stationary state it can be given by following equation.

`m_evr=nh/(2π)`

Where n = 1, 2, 3, …………………

Here, m_e is mass of electron, v is velocity and r is the radius of orbit in which electron is moving.

This equation shows that electron can move only in those orbits for which its angular momentum is integral multiple of `h/2π`. In other words, angular momentum is quantized.

According to Bohr’s theory of hydrogen atom

The stationary states for electron are numbered n = 1, 2, 3 ………..These integral numbers are known as Principal Quantum Numbers.

The radii of stationary states are expressed as r_n = n²a₀ where a₀ = 52.9 pm. So, the radius of the first stationary stage, called the Bohr orbit is 52.9 pm.

The energy of the stationary state is the most important property associated with the electron. It is given by following expression.

`E_n=-R_H(1/(n^2))` n = 1, 2, 3, …………

Where R_H is called Rydberg constant and its value is 2.18 × 10^-18 J.

Energy of the lowest state is

`E_1=-2.18xx10^(-18)(1/(1^2))`

`=2.18xx10^(-18)` J

Energy of the stationary state for n = 2 will be

`E_2=-2.18xx10^(-18)(1/(2^2))`

`=0.545xx10^(-18)` J

When the electron is free from the influence of nucleus, the energy is taken as zero. In this situation, the electron is associated with the stationary state of Principal Quantum number = n = ∞ and is called as ionized hydrogen atom.

Limitations of Bohr’s Model

Bohr’s model fails to account for finer details of hydrogen atom spectrum observed by using sophisticated spectroscopic techniques.
It is unable to explain the spectrum of atoms other than hydrogen.
Bohr’s model fails to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect).
Bohr’s model could not explain the ability of atoms to form molecules by chemical bonds.