An unstable nucleus contains excess of neutrons, and this causes neutron transforming into proton by emitting an electron.

When a β particle is emitted by an atom, its atomic number increases by 1 and mass number doesn’t change.

Rutherford and Soddy’s law of β decay states that “whenever an β particle is emitted from a radioactive nucleus, the atomic number decreases by 1 and the mass number remains the same and the position of the element shifts by one place to right in the periodic table”.

When an α (alpha) particle is emitted by an atom, its atomic number (Z) decreases by 2 and mass number (A) decreases by 4.

Here P is called the parent nucleus.
D is called as daughter nucleus.

In the above example Uranium is the parent nucleus and thorium is the daughter nucleus.

Rutherford and Soddy’s law of α emission states that “whenever an α particle is emitted from a radioactive nucleus, the atomic number decreases by 2 and the mass number decreases by 4 and the position of the element shifts by two places to left in the periodic table”.

Mass defect is the difference between the actual mass of nucleus and sum of masses of constituent nucleons.

The formula for Mass defect is given as,
m = [Z m_p + (A – Z)m_n] – M

M = mass of nucleus
A = mas number                           
m_p = mass of proton
Z = atomic number                              
(A – Z) = number of neutron
m_n = mass of neutron                          

In atomic physics, The Rydberg formula is used to describe the wavelengths of spectral lines of many chemical elements.

The modified Rydberg formula given below is used for any hydrogen-like chemical elements.

λ_vac= the wavelength of the light emitted in vacuum;

R = the Rydberg constant for this element;

Z = the atomic number, i.e. the number of protons in the atomic nucleus of this element;

n₁and n₂= integers such that n₁< n₂, corresponding to the principal quantum numbers of the orbitals occupied before and after.

In atomic physics, The Rydberg formula is used to describe the wavelengths of spectral lines of many chemical elements.

The modified Rydberg formula given below is used for hydrogen element.

λ_vac = the wavelength of the light emitted in vacuum;

R = the Rydberg constant for this element;

n₁ and n₂ = integers such that n₁< n₂, corresponding to the principal quantum numbers of the orbitals occupied before and after.