How do you calculate the average atomic mass of an element with four isotopes if you are given the masses of the isotopes?

Answer 1

One needs to know the proportion of each isotope in the substance under question. If these four proportions are c_i where i ranges from 1..4, and the atomic masses are m_i, then the result is:

<m> = \sum_{i=1}^4 m_i \times c_i

or,

<m> = m_1 x c_1 + m_2 x c_2 + m_3 x c_3 + m_4 x c_4

where <m> is the average mass.

Remember that m_i are numbers which are proportions, so for, say, 13%, you should use 0.13

As an example, let's look at oxygen isotopes. Oxygen has three isotopes. The average weight calculated this way is:

<m> = 16 x 0.9976 + 17 x 0.00039 + 18 x 0.00201

<m> = 16.004

However, the reported average weight on this page is 15.9994amu. The reason there is a discrepancy here is because O16 does not have an atomic weight of 16amu due to mass loss through nuclear binding, and it is slightly less than 16. Pursuing that question is outside the scope of this answer, and this is not your question because you are given the masses of the isotopes. But the one missing piece are the relative amounts, c_i. Those seem to be pretty easy to get if you know the element, using wikipedia.

Answer 2

To calculate the average Atomic Mass of an element with four isotopes, you first multiply the mass of each isotope by its abundance as a decimal, then add the products together to find the atomic mass. This formula can be expressed as ((mass isotope 1 x abundance) + (mass isotope 2 x abundance) + (mass isotope 3 x abundance) + (mass isotope 4 x abundance)).