Sodium only has one naturally occuring isotope, Na23 , with a relative atomic mass of 22.9898 u. A synthetic, radioactive isotope of sodium, Na22 , is used in positron emission tomography. Na22 has a relative atomic mass of 21.9944 u.

A 1.3476 g sample of sodium containing a mixture of Na23 and Na22 has an apparent "atomic mass" of 22.9501 u . Find the mass of Na22 contained in this sample.

We have a sample with 2 isotopes of sodium. Na22 with a relative atomic mass of 21.9944 u and Na23 with a relative atomic mass of 22.9898 u. Let "x" be the fractional abundance of Na22 and "1-x" the fractional abundance of Na23. If the apparent atomic mass is 22.9501 u, we can state the following expression.

[tex]mNa22 \times x + mNa23 \times (1-x) = 22.9501u\\21.9944u \times x + 22.9898u \times (1-x) = 22.9501u\\x=0.039883[/tex]

The mass of the sample is 1.3476 g. We can find the mass of Na22 in the sample by multiplying it by its fractional abundance.

[tex]1.3476g \times 0.039883 = 0.053746 g[/tex]

The mass of Na22 in the sample is 0.053746 g.

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