Question

If initially there are 300 grams of a radioactive substance and after 5 years there are 200 g remaining, how much time must elape before only 10 grams remain?

Answer 1

The radioactive substance will take approximately 25 years to decrease from 200 g to 10 g.

Step-by-step explanation:

The quantity of radioactive nuclei decreases by half in each half-life. So, in the given scenario, the radioactive substance has decreased from 300 g to 200 g in 5 years. This means that the 300 g has gone through one half-life in 5 years.

To find how long it takes for the substance to decrease from 200 g to 10 g, we need to determine how many half-lives it takes. We can set up the following equation: 200 g * (1/2)^n = 10 g, where n represents the number of half-lives. Solving for n, we get:

200 * (1/2)^n = 10 => (1/2)^n = 10/200 => (1/2)^n = 1/20 => n = log(1/20)/log(1/2)

Using a calculator, n is approximately equal to 4.32. Since we can't have a fraction of a half-life, we round up to 5. Therefore, it will take approximately 5 half-lives for the substance to decrease from 200 g to 10 g. Since each half-life is 5 years, the total time it will take is 5 x 5 = 25 years.