Answer to Question #96544 in General Chemistry for Kaylee Williams

Question

Sodium only has one naturally occurring isotope, 23Na, with a relative atomic mass of 22.9898 u. A synthetic l, radioactive isotope of sodium, 22Na, is used in positron emission tomography. 22Na has a relative atomic mass of 21.9944 u. A 2.0878 g sample of sodium containing a mixture of 23Na and 22Na has an apparent “atomic mass” of 22.9665 u. Find the mass of 22Na contained in this sample.

Answer 1

Let x to be fractional abundance of $^{23}Na$

Let 1-x to be fractional abundance of $^{22}Na$

Then

$$22.9898x + 21.9944 (1-x) = 22.9665$$

$$x= 0.9766$$

m($^{23}Na$ )= $2.0878\times x =2.0878\times0.9766 = 2.0389 g$