Question

The half-life of radium-226 is 1620 years. Knowing this, you can determine the percentage of an original sample of

Ra-226 that will remain after 4860 years have passed. This percent is?

Answer 1

12.5%

Step-by-step explanation:

We must first determine the fraction of radium-226 remaining after 4860 years. We can obtain that from;

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

Where;

Nt= amount of radium-226 remaining after time t

No= amount of radium-226 available at time t=0

t1/2 = half life of radium-226= 1620 years.

t= time taken for Nt amount of radium-226 to remain= 4860 years

Substituting values;

Nt/No = (1/2)^ 4860/1620

Nt/No = (1/2)^3

Nt/No = 1/8

The percentage of the original sample remaining after 4860 years= 1/8 ×100 = 12.5%

Hence 12.5% of radium-226 remains after 4860 years.