If a radioactive source has a half life of 2 hours how long will it take for the activity to go from 200 to 25?

It takes 6h to the radioactive source decrease its activity from 200 to 25

Explanation:

The equation that describes the readioactive decay is:

Ln [A] = -kt + Ln [A]₀

Where [A] could be taken as activity of the source after time t, [A]₀ is initial activity and k is decay constant.

Decay constant could be written as:

k = ln2 / Half-life

k = ln 2 / 2h

k = 0.3466h⁻¹

Replacing in decay equation:

Ln [25] = -0.3466h⁻¹t + Ln [200]

-2.0794 = -0.3466h⁻¹t

6h = t

It takes 6h to the radioactive source decrease its activity from 200 to 25