A sample of radium-226 will decay to ¼ of its original amount after 3200 years. What is the half-life of radium-226?

Answer;

1600 years

Explanation; Half life is the time taken for a radioactive isotope to decay by half of its original amount. We can use the formula; N = O * (1/2) ^n; where N is the new mass, O is the original amount and n is the number of half lives. A sample of radium-226 takes 3200 years to decay to 1/4 of its original amount.

Therefore;

1/4 = 1 * (1/2) ^n

1/4 = (1/2) ^n

n = 2

Thus; 3200 years is equivalent to 2 half lives.

Hence, the half life of radium-226 is 1600 years