Question

The halflife of a radioactive isotope is 20.0 minutes. How much of a 1.00 gram sample of this isotope remains after 1.00 hour?

Answer 1

`0.125color(white)(l)"g"`

Explanation:

There are

`1.00color(white)(l)color(red)(cancel(color(black)("hours")))*(60.0color(white)(l)color(purple)(cancel(color(black)("minutes"))))/(1.00color(white)(l)color(red)(cancel(color(black)("hours")))) cdot (1color(white)(l) "halflife")/(20.0color(white)(l)color(purple)(cancel(color(black)("minutes"))))=color(navy)(3)color(white)(l) "halflives"`

in `1.00color(white)(l)"hours"` of time.

The mass of the sample halves every halflife of the decay. That is: given an initial mass of `m_0`, the remaining sample will have mass

`m=(1/2)^(n)*m_0`

after `n` halflives.

Therefore, the sample will have a mass of

`m=(1/2)^color(navy)(3)*1.00color(white)(l) "g"`
`color(white)(m)=1/8*1.00 color(white)(l) "g"`
`color(white)(m)=0.125 color(white)(l) "g"`

after an hour.