Question

The half-life of a certain element is 100 days. How many half-lives will it be before only one-eighth of this element remains?

Answer 1

Answer:

3

Explanation:

The half-life is the time it takes for the amount of radioactive isotope to halve. Therefore, we have:

- After 1 half-life, only 1/2 of the element will be left

- After 2 half-lives, only 1/4 of the element will be left

- After 3 half-lives, only 1/8 of the element will be left

So, it will take 3 half-lives for the element to become 1/8 of its original amount.

Mathematically, this can be also verified by using the equation

$\frac{N(t)}{N_0}=(\frac{1}{2})^\frac{t}{\tau_{1/2}}$

where

N(t) is the amount of the element left at time t

N0 is the initial amount of the element

$\tau_{1/2}$ is the half-life

Substituting $t=3\tau_{1/2}$ (3 half-lives), we find

$\frac{N(t)}{N_0}=(\frac{1}{2})^3=\frac{1}{8}$