Question

A radioactive substance's half-life is the amount of time needed for half (or 50%) of the substance to decay. Let's say we have a radioactive substance with a half life of 20 years. (a) what percent of the substance would be radioactive after 40 years?

Answer 1

Answer:

25 percent of the substance would be radioactive after 40 years.

Step-by-step explanation:

Initial mass of the substance = $N_o$

Half life of the substance =$\t_{1/2}=20 years$

Mass of substance left after 40 years = N

t = 40 years

Radio active decay follows first order kinetics, so:

$N=N_o\times e^{-\frac{0.693}{t_{1/2}}\times t}$

$N=N_o\times e^{-\frac{0.693}{20 years}\times 40 years}$

$\frac{N}{N_o}=0.2500$

Percent of the substance would be radioactive after 40 years:

$0.2500\times 100= 25.00\%$