Question

Aradioactive isotope has a half-life of Tyears. How long will it take theactivity to reduce to a) 3.125%, b) 1% of its original value?

Answer 1

Half-life of theradioactive isotope = Tyears

Original amount of the radioactive isotope = N₀

(a) Afterdecay, the amount of the radioactive isotope = N

Itis given that only 3.125% of N₀remains after decay. Hence, we canwrite:

Where,

λ= Decay constant

t= Time

Hence,the isotope will take about 5Tyears to reduce to 3.125% of its original value.

(b) Afterdecay, the amount of the radioactive isotope = N

Itis given that only 1% of N₀remains after decay. Hence, we canwrite:

Since,λ= 0.693/T

Hence,the isotope will take about 6.645Tyears to reduce to 1% of its original value.