Question

The half-life of rhodium is about 30 seconds. After 90 seconds, what fraction of the original amount of rhodium remains?

a) 1/2
b) 1/3
c) 1/4
d) 1/8

Answer 1

After three half-lives of 30 seconds each, the fraction of the original amount of rhodium that remains is 1/8.

Step-by-step explanation:

The Fraction of Rhodium Remaining After 90 Seconds

The half-life of rhodium is about 30 seconds. Therefore, after 90 seconds, which is equivalent to three half-lives, we can calculate the fraction of rhodium that remains. Initially, we have N atoms of rhodium. After one half-life (30 seconds), we have N/2 remaining. After two half-lives (60 seconds), we are left with N/4. Lastly, after three half-lives (90 seconds), the amount of rhodium is reduced to N/8. Hence, the fraction of the original amount of rhodium that remains after 90 seconds is 1/8.