In a periodic table, the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are ²⁴₁₂Mg (23.98504u), ²⁵₁₂Mg (24.98584u) and ²⁶₁₂Mg (25.98259u). The natural abundance of ²⁴₁₂Mg is 78.99% by mass. Calculate the abundances of other two isotopes.

Given that,

Average atomic mass of magnesium, m_avg = 24.312 u

Mass of magnesium isotope (m₁),

Mass of magnesium isotope (m₂),

Mass of magnesium isotope (m₃),

Abundance of magnesium isotope (n₁),

We know that sum of abundances of all isotopes together is equal to total magnesium available on earth, 100% magnesium.

Let, Abundance of magnesium isotope (n₂)

Thus, Abundance of isotope (n₃),

We have the relation for the average atomic mass is,

∴

⇒

⇒ -9.272526 u = -0.99675x u

∴ = Abundance of isotope (n₂),

Thus, Abundance of isotope (n₃),