The following isotopes (listed with their half-lives) have been used in the medical and biological sciences. Arrange these isotopes greatest to least decay activity. (Use the appropriate <, =, or > symbol to separate substances in the list.)
^3H (12.2 years)
^24Na (15 years)
^131I (8 days)
^60Co (5.3 years)
^14C (5730 years)
This looks easy enough. Wouldn't you think the one with the greatest decay rate (8 days) would be first and the one with the longest decay rate (5,730 years) would be last?
To arrange the isotopes from greatest to least decay activity, we need to compare their half-lives. The shorter the half-life, the greater the decay activity. Here's how we can compare them:
1. ^131I (8 days) is the shortest half-life, so it has the greatest decay activity.
2. ^60Co (5.3 years) has a longer half-life than ^131I, so it has less decay activity. We can represent this by writing "^131I > ^60Co".
3. ^3H (12.2 years) has a longer half-life than ^60Co, so it has even less decay activity. We can represent this by writing "^131I > ^60Co > ^3H".
4. ^24Na (15 years) has a longer half-life than ^3H, so it has less decay activity. We can represent this by writing "^131I > ^60Co > ^3H > ^24Na".
5. ^14C (5730 years) has the longest half-life among all the isotopes, so it has the least decay activity. We can represent this by writing "^131I > ^60Co > ^3H > ^24Na > ^14C".
Therefore, the arrangement from greatest to least decay activity is:
^131I > ^60Co > ^3H > ^24Na > ^14C.