In a periodic table the average atomic mass of magnesium is givenas 24.312 u. The average value is based on their relative naturalabundance on earth. The three isotopes and their masses are 2412Mg(23.98504u), 2512Mg (24.98584u) and 2612Mg (25.98259u). The naturalabundance of 2412Mg is 78.99% by mass. Calculate the abundancesof other two isotopes.
Given, the average atomic mass of magnesium is 24.312 u , and the isotopes and their masses are M 12 24 g ( 23.98504 u ) , M 12 25 g ( 24.98584 u ) and M 12 26 g ( 25.98259 u ) .
The natural abundance of M 12 24 g is 78.99 % by mass.
Let the abundance of M 12 25 g be x % , then the abundance of M 12 26 g = ( 100 − x − 78.99 ) % = ( 21.01 − x ) %
The relation for average atomic mass is represented as,
m = m 1 n 1 + m 2 n 2 + m 2 n 3 n 1 + n 2 + n 3
Here, m 1 , m 2 and m 3 are the respective masses of the three isotopes M 12 24 g , M 12 25 g and M 12 26 g : and n 1 , n 2 and n 3 are the respective abundance of the isotopes M 12 24 g , M 12 25 g and M 12 26 g .
Substituting the values in the above expression, we get:
24.312 = 23.985 × 78.99 + 24.985 × x + 25.983 × ( 21.01 − x ) 78.99 + x + 21.01 − x 24.312 = 1894.57 × 78.99 + 24.985 x + 545.89 − 25.892 x 100 0.9976 x = 9.2725 x = 9.28 %
Thus, the abundance of M 12 25 g is,
( 21.01 − x ) % = ( 21.01 − 9.28 ) % = 11.71 %
Hence, the abundance of M 12 25 g is 9.28 % and M 12 26 g is 11.71 %
Given, the average atomic mass of magnesium is
The natural abundance of
Let the abundance of
The relation for average atomic mass is represented as,
Here,
Substituting the values in the above expression, we get:
Thus, the abundance of
Hence, the abundance of
