Question

You have 480 grams of a radioactive kind of samarium. If its half-life is 90 years,

how much will be left after 180 years?​

Answer 1

120 grams will be left after 180 years.

Explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

`N(t)=N_0((1)/(2))^(t)/(t_(1/2))`

where,

`N(t)` = quantity of the substance remaining

`N_0` = initial quantity of the substance

`t` = time elapsed

`t_(1/2)` = half life of the substance

From the information given we know that:

• The initial quantity is 480 g,
• The half-life is 90 years,
• 180 years is the time elapsed.

And we want to find how much will be left. For this we use the above formula.

`N(t)=480\left((1)/(2)\right)^{(180)/(90)}\\\\N(t)=480\left((1)/(2)\right)^2\\\\N(t)=480\cdot (1)/(2^2)=120`

120 grams will be left after 180 years.