Half Life In DAYS

Question

A certain radioactive isotope has leaked into a small stream. OneOne hundred days after the​ leak, 99​%

of the original amount of the substance remained. Determine the​ half-life of this radioactive isotope.

Answer 1

Fraction remaining = 0.5ⁿ where n = number of half lives that have elapsed.

Fraction remaining = 99% = 0.99

n = ?

0.99 = 0.5ⁿ

log 0.99 = n log 0.5

-0.004365 = -0.30103n

n = 0.01450 days

n = 24 hrs/day x 0.01450 days = 0.348 hours

n = 0.348 hours x 60 min/hour = 20.88 minutes (20 minutes 53 seconds)