Question

If a substance has a half life of 58 years and starts with 500 g radioactive, how much remains radioactive after 30 years?

Answer 1

A = 349 g.

Step-by-step explanation:

Hello there!

In this case, since the radioactive decay kinetic model is based on the first-order kinetics whose integrated rate law is:

`A=Ao*exp(-kt)`

We can firstly calculate the rate constant given the half-life as shown below:

`k=(ln(2))/(t_(1/2)) =(ln(2))/(58year)=0.012year^(-1)`

Therefore, we can next plug in the rate constant, elapsed time and initial mass of the radioactive to obtain:

`A=500g*exp(-0.012year^(-1) *30year)\\\\A=349g`

Regards!