Question

Calculating Half-Life

Answer 1

Complete Question:

A sample of radium-226 will decay to 1/4 of its original amount after 3200 years. What is the half-life of radium-226?

Answer:

1,600 years is the half life of radium-226.

Explanation:

The half-life (symbol $t_{1 / 2}$)  is the time it requires or the time taken to reduce the amount to half of its original value. The term is often used in nuclear physics to describe how quickly unstable atoms are radioactive degrading or how long stable atoms remain.

There will be 100% presence of sample in zero half-life.

In first half-life, 50% available of sample ($\frac{1}{2}$ left from the original)

Then second half life, 25% available of sample ($\frac{1}{4}$ left from the original)

Here, given sample of radium-226 will decay to 1/4 of its original amount after 3200 years.

So, after two half life, sample of radium-226 will decay to 1/4 of its original amount. Hence, simply divide 3200 by 2 to find half-life.

           $\frac{3200}{2}=1600 \text { years }$