Radium has a half-life of 1500 years. How long will it take for 250kg of Radium to decay down to less than 10kg

6967 years

Explanation:

The radioactive substance left after a periodical t year can be expressed by using the formula:

here;

= the radioactive initial value.

We need to understand that provided that the radioactive substance will get reduced to half of the provided initial amount  after a periodic time, Then:

the half-life of the radioactive substance left is:

Given that:

the half-life = 1500 years

Divide both sides by

Then, find the natural logarithm of both side;

k = 0.000462

So, after a particular (t) time, a 250 kg radium sample was reduced to 10 kg;

Then:

From both sides, finding the natural logarithm, we have:

In(0.04) = -0.000462t

t = 6967.26

Thus, it will take approximately 6967 years for a 250 kg radium sample to get reduced to 10 kg.