Answer to Question #211624 in Differential Equations for Vivek

Question

The rate constant for the radioactive disintegration of ⁶⁰₂₇Co is 0.1317 year".

Calculate the mass of .₂₇⁶⁰Co that will remain after 21.04 years out of 1 gram sample.

Answer 1

half life of reaction = $\frac{0.693}{k}$

Here,

k = Reaction constant = 0.1317

So, half life will be = $\frac{0.693}{0.1317}$ = 5.26 years.

So, in 5.26 years given sample will be reduced to half.

So, in first half life (after 5.26 years), sample will be reduced to 0.5 grams.

In 2nd half life (after 5.26 x 2 = 10.52) years, sample will be reduced to 0.25 grams.

In 3rd half life (after 5.26 x 3 = 15.78) years, sample will be reduced to 0.125 grams.

In 4th half life (after 5.26 x 4 = 21.04) years, sample will be reduced to 0.0625 grams.

Hence, the answer will be 0.0625 grams.