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Natural boron is 20 % boron-10 and 80 % boron-11, with an average atomic mass of 10.8 u…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Natural boron is $20\ \%$ boron-10 and $80\ \%$ boron-11, with an average atomic mass of $10.8\ \text{u}$ . Boron-10 soaks up neutrons, so the boron in the control rods of a nuclear reactor is enriched to $90\ \%$ boron-10 and $10\ \%$ boron-11.

Find the average atomic mass of the enriched boron.
How much lighter is it than natural boron?

Need a reminder? The key ideaShow

The atomic mass of an element is the average of its isotopes' masses, weighted by how common each one is: $\text{average} = \dfrac{\sum (\text{mass number} \times \text{percentage})}{100}$ . When the average is known, let $x$ be one percentage and solve for it.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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