# The half-life of a certain radioactive isotope is 6 hours. If we start out with 100 grams of the isotope, how many grams will be left after 1 day?

##### 1 Answer
Apr 20, 2018

For half life the best way to go about it is to follow the general half life equation:

$y = x {\left(.5\right)}^{\frac{t}{n}}$

Where n is the half life time, in this case 6 hours and t is the time elapsed.

This equation can be better understood by understanding its mechanism: half of the initial mass will remain when you raise .5 to the power of 1, which means that when t=n, the power will be 1 and half the initial amount will be present.

Your initial mass is 100 grams, your half life time is 6 hours, and your time elapsed is 1 day or 24 hours. (Make sure your time elapsed is the same units as the half life time)

Putting all these in yields

$y = \left(100\right) \cdot {\left(.5\right)}^{\frac{24}{6}}$

$y = \left(100\right) \cdot {\left(.5\right)}^{4}$

$y = 6.25$

Your mass is 6.25 grams after 24 hours.