Question

The half-life of cobalt-60 is 5.26 years. If 50 g are left after 15.8 years, how many grams were in the original sample?

Answer 1

`m_i= 400 \ grams`

Explanation:

The following formula relates the mass remaining of the radioiosotope to the original mass:

`m_i=m_rxx2^n`

Where:

`m_i : " is the initial mass of the radioisotope"`
`m_r: " is the mass remaining of the radioisotope after n periods"`
`n :" is the number of periods"`
`n =( "time")/ ("half life" )`

First, find the number of periods.

`n= (15.8 " years")/(5.26 " years")`
`n = 3`
Then plug in the values in the original formula

`m_i=m_rxx2^n`
`m_i = 50 xx 2^3`
`m_i= 400 \ grams`

`-------------------`

A quick approach

Knowing that the time represents three periods

`50 -> 100 -> 200 -> 400 \ grams`