Question

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

Answer 1

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

Answer 2

4860 years

Step-by-step explanation:

From

N/No = (1/2)^t/t1/2

Where:

No= mass as time t=0

N= mass at time t

t= time

t1/2= half life

0.125/1 = (1/2)^t/1620

1/8 = (1/2)^t/1620

(1/2)^3= (1/2)^t/1620

3= t/1620

t= 3×1620

t= 4860 years