Question

The half life of thorium-234 is 24 days. If you started with 20g, how long would it take to have 5g remaining?

Answer 1

It would take 48 days for a 20g sample of thorium-234 to decay to 5g, as it takes two half-lives (24 days each) for the sample to reduce from 20g to 5g.

Step-by-step explanation:

The half-life of thorium-234 (Th) is 24 days. To determine how long it would take for a 20g sample to decay until only 5g remains, we can use the concept of half-lives. A half-life is the time required for half of the radioactive substance to decay.

Since 20g decays to 10g after one half-life (24 days), it decays to 5g after two half-lives. Therefore, we simply multiply the half-life duration by the number of half-lives required to get from 20g to 5g:

Calculation:

1. First half-life: 20g to 10g (24 days)
2. Second half-life: 10g to 5g (24 days)

Adding the durations together:

24 days + 24 days = 48 days

So, it would take 48 days for a 20g sample of Th to decay to 5g.