Suppose that 30 percent of element Y exists as ¹³⁰Y and 70 percent of it exists as ¹⁴⁰Y. What is the atomic weight of element Y in atomic mass units? A) 130, B) 133, C) 137, D) 140, or E) 270.
Firstly, we can assume that we’re dealing with a hypothetical element. There is an element with symbol Y called yttrium. But the heaviest isotope of yttrium only has a mass number of 108. The atomic mass of an element is simply the average mass of atoms of that element based on the abundance of different isotopes. These abundances are usually determined by taking samples on earth.
So in most cases, atomic weights are only relevant to earthbound materials. In this case, we know that 30 percent of all the atoms of element Y are ¹³⁰Y and 70 percent of them are ¹⁴⁰Y. The 130 and the 140 refer to the mass number of the particular isotope. The mass number refers simply to the number of protons and neutrons in each nucleus of that isotope.
Protons and neutrons have a mass of about one unified atomic mass unit. So the mass for each atom of element Y with a mass number of 130 is about 130 unified atomic mass units. And the mass of an atom of ¹⁴⁰Y is 140 unified atomic mass units. When considering the mass of an atom, we tend to ignore the mass of electrons because, relatively speaking, electrons have very little mass.
For the next bit, let’s imagine that we have exactly 100 atoms of Y. The question tells us that 30 percent of all atoms of Y are ¹³⁰Y. So 30 out of 100 atoms would be ¹³⁰Y. So the remainder, the other 70 percent, are atoms of ¹⁴⁰Y. We can work out the atomic weight by working out the mass of these 100 atoms of Y and then just divide by 100. That’s equal to 30 times the mass of the ¹³⁰Y atoms, which is 130 unified atomic mass units, plus 70 times the mass of the ¹⁴⁰Y atoms, which is 140 unified atomic mass units, all divided by 100. 30 times 130 is 3900, and 70 times 140 is 9800. This gives us 13700 unified atomic mass units divided by 100, meaning the average mass of an atom of element Y and therefore the atomic weight is 137 unified atomic mass units. Subtract the units, and our final answer is 137.