Radium has a half-life of 1,620 years. In how many years will a 1 kg sample of radium decay and reduce to 0.125 kg of radium?

a. 1,620 years

b. 3,240 years

c. 4,860 years

d. 6,480 years

We can calculate years by using the half-life equation. It is expressed as:

A = Ao e^-kt

where A is the amount left at t years, Ao is the initial concentration, and k is a constant.

From the half-life data, we can calculate for k.

1/2 (Ao) = Ao e^-k (1620)

k = 4.28 x 10^-4

0.125 = 1 e^ - 4.28 x 10^-4 (t)

t = 4259 years