Sodium only has one naturally occuring isotope, 23 Na, with a relative atomic mass of 22.9898 u. A synthetic, radioactive isotope of sodium, 22 Na, is used in positron emission tomography. 22 Na has a relative atomic mass of 21.9944 u. A 1.8385 g sample of sodium containing a mixture of 23 Na and 22 Na has an apparent "atomic mass" of 22.9573 u. Find the mass of 22 Na contained in this sample?

Mass of 22-Na contained in the sample = 0.0599 g

Explanation:

Mass of the isotope mixture = 1.8385g

Isotope mixture has apparent mass of 22.9573 u

23-Na has a relative atomic mass of 22.9898 u

22-Na has a relative atomic mass of 21.9944 u

Let the relative abundance of 23-Na be X

Then the relative abundance of 22-Na would be (1-X)

21.9944 (1-X) + 22.9898 X = 22.9573

21.9944 - 21.9944X + 22.9898X = 22.9573

22.9898X - 21.9944X = 22.9573 - 21.9944

0.9954X = 0.9639

X = 0.9674

Relative abundance of 23-Na = 0.9674

Relative abundance of 22-Na = 1 - 0.9674 = 0.0326

Mass of 22-Na in the 1.8385g of sample is

Relative abundance of 22-Na * Mass of sample = 0.0326 * 1.8385g = 0.0599 g