Spontaneous emission

Let us consider two energy levels E₁ and E₂ in a material. For convenience, E₁ is taken to be the ground level. E₂ is greater than E₁. ( E₂ > E₁ ) The two levels of energy under consideration can be any two of the unlimited numbers of levels of energy that can be possessed by any material. 

E₁ = Energy level 1 ( Ground state )

E₂ = Energy level 2 ( Excite state ) 

h = Plank's constant

v = Frequency of radiated energy 

When the particle or atom of the material is excited, it can remain in the excited state for a limited time known as a lifetime. The lifetime of the excited hydrogen atoms is of the order of 10^-8 sec. Usually, the number of excited particles in a system is smaller than the non-excited particles. The time during which a particle can exist in the ground state is unlimited. The particle at the excitement level is more unstable as compared to that at the ground level. Naturally, there is a tendency for the particle to come back to ground level. When it comes back to ground level, the particle releases some amount of energy. When this energy is released in the form of electromagnetic waves, we call it spontaneous emission of energy. The frequency of the radiated wave is given by :

v = ( E₂ - E₁ / h ) 

OR 

hv = ( E₂ - E₁ ) 

Note: Radiative emission is just one of the two possible ways for the atom to decay. The decay can also occur in a non-radiative manner. In the non-radiative transition, the difference in energy levels E₂ and E₁ can be experienced in regions other than electromagnetic. 

You can also look at the difference between spontaneous and stipulated emission.