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"#

There exist

#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.

Consequently, the sample's mass will be

#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"#

an hour later.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Mateo Aguilar

One eighth, or 0.125 grams, of the radioactive isotope is still present after one hour.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.