Magnesium (average atomic mass = 24.3050 amu) consists of three isotopes with masses 23.9850 amu, 24.9858 amu, and 25.9826 amu. The abundance of the middle isotope is 10.00%. Estimate the abundances of the other isotopes.

Answer: The first isotope has a relative abundance of 79% and last isotope has a relative abundance of 11%

Explanation: Given that the average atomic mass (M) of magnesium

= 24.3050amu

Mass of first isotope (M1) = 23.9850amu

Mass of middle isotope (M2) = 24.9858amu

Mass of last isotope (M3) = 25.9826amu

Total abundance = 1

Abundance of middle isotope = 0.10

Let abundance of first and last isotope be x and y respectively.

x+0.10+y = 1

x = 0.90-y

M = M1 * % abundance of first isotope + M2 * % of middle isotope + M3 * % of last isotope

24.03050 = 23.985 * x + 24.9858 * 0.10 + 25.9826*y

Substitute x = 0.90-y

Then

y = 0.11

Since y=0.11, then

x = 0.90-0.11

x=0.79

Therefore the relative abundance of the first isotope = 11% and the relative abundance of the last isotope = 79%