Question

Find the half-life of a radioactive element, if its activity decreases for 1 month by 20%.

Answer 1

Initial activity of the radioactive element = N₀

The activity of the radioactive element decreases by 20% in 1 month that is only 80% is left.

Activity of the radioactive element after 1 month = N = 0.8N₀

Time period = 1 month

Half-life of the radioactive element = T_1/2

Decay constant =

Taking natural log on both sides,

T_1/2 = 3.106 months

Half-life of the radioactive element = 3.106 months