Challenge Level

Do you think it will be easy to distinguish between each of the isotopes of cobalt?

Imagine to start that that the sample consists of a single isotope of the cobalt. Would such a sample have too much or too little cobalt at each of the times indicated? How could you adjust the sample to bring it in line with the numbers indicated?

This problem makes use of chemistry concepts found in A-level. The main fact of importance is that in each half-life half of the cobalt will transform into other matter, the vast majority of which will remain in the sample. Mathematically, you will need to use linear algebra, simultaneous equations such as typically encountered at post-16 level, although a simpler numerical analysis will allow younger students to engage with the problem.

Imagine to start that that the sample consists of a single isotope of the cobalt. Would such a sample have too much or too little cobalt at each of the times indicated? How could you adjust the sample to bring it in line with the numbers indicated?

This problem makes use of chemistry concepts found in A-level. The main fact of importance is that in each half-life half of the cobalt will transform into other matter, the vast majority of which will remain in the sample. Mathematically, you will need to use linear algebra, simultaneous equations such as typically encountered at post-16 level, although a simpler numerical analysis will allow younger students to engage with the problem.