Given specimens neon-24 and bismuth-211 (\(\left( {{t_{1/2}} = 3.38\;{\rm{min}}} \right)\)\(\left. {{t_{1/2}} = 2.14\;{\rm{min}}} \right)\)of equal mass, which one would have greater activity and why?

A physical body's mass is the amount of matter it contains. It's also a measure of the body's inertia or resistance to acceleration (velocity change) when a net force is applied.

For this task, we can use the next formula:

\(t = \frac{1}{\lambda }\ln \frac{{{n_0}}}{{{n_t}}}\)

Since the atomic mass of both substances is equal, the concentration of nuclides will be equal.

There is also a formula for the decay constant:

\(\lambda = \frac{{\ln (2)}}{{{t_{1/2}}}}\)

Since we have two isotopes, there is an expression used to find the activity of isotopes: activity \( = \lambda \cdot N\)

In that formula, we can put the decay constant from above:

\({\mathop{\rm activity}\nolimits} = \frac{{\ln (2)}}{{{t_{1/2}}}} \cdot N\)

From that, we can see that activity is inversely proportional to the half-life:

\({\mathop{\rm activity}\nolimits} \propto \frac{{\ln (2)}}{{{t_{1/2}}}}\)

As a result, the activity will be lower if we have a longer half-life. Because bismuth-\(21\) has a shorter half-life, it has higher activity than neon-24.