# The half-life of cesium-137 is 30 years. Suppose we have a 120-mg sample. Find the mass that remains after #t# years. How much of the sample remains after 90 years? After how long will only 1 mg remain?

##### 1 Answer

#### Explanation:

**(a) Mass after t years**

The formula for calculating the amount remaining after a number of half-lives,

#color(blue)(bar(ul(|color(white)(a/a)"A" = "A"_0/2^ncolor(white)(a/a)|)))" "#

where

This gives

#"A" = A_0/2^( t/t_½)#

∴

**(b) Mass after 90 yr**

**(c) Time for 1 mg remaining**