Group Displacement Law

According to this law, "When an α - particle is emitted the daughter element has atomic number 2 units less than that of the parent element. It is consequently displaced two places to the left in the periodic table. When a β-particle is emitted, the daughter element has an atomic number 1 unit higher than that of the parent element. It is consequently displaced one place to the right in the periodic table.

Counting of number of α and β particles in a radioactive transformation

Parent element Daughter element

Number of α - particles = =

Number of β-particles: Let 'x' β-particles and 'y' α - particles be emitted

Atomic number of parent element – 2y + x = Atomic number of daughter element

Z₁ – 2y + x = Z₂

∴x = (Z₂ – Z₁ + 2y)

Further Reading : 

1. Question of Group Displacement Law
2. Some Complex First Order Reaction
3. Radioactivity