Some Properties of Atoms — Question 3

Question 3

An isotopic abundance can be inferred from a mean atomic mass

A hypothetical element has only isotopes of masses $62.0\,\mathrm u$ and $65.0\,\mathrm u$. Its measured mean atomic mass is $63.2\,\mathrm u$. Treat the quoted masses as exact in this model.

1. Find the number fraction of the heavier isotope.

2. Find its mass fraction in a macroscopic sample.

Question 3 - Solution

An isotopic abundance can be inferred from a mean atomic mass

(a) Method and calculation

$$\bar m=(1-x)m_l+xm_h=m_l+x(m_h-m_l).$$$$\boxed{x=(63.2-62.0)/(65.0-62.0)=0.400}.$$

(b) Interpretation and further calculation

$$w_h=\frac{Nxm_h}{N\bar m}=\frac{xm_h}{\bar m}.$$$$\boxed{w_h=26.0/63.2=0.4114}.$$

Physical check

Number fractions weight the mean mass; mass fractions weight the sample mass. The heavier isotope has a larger mass fraction than number fraction.