Question

The half-life of a radioactive isotope is 20.0 minutes. What is the total amount of a 1.00-gram sample of this sample of this isotope remaining after 1.00 hour?

Answer 1

Well, looking at it non-analytically...

After 1.00 hours, how many half-lifes have passed? 3.

So the amount of substance would have been halved three times...

\[1.00g \rightarrow 0.50g \rightarrow 0.25g \rightarrow 0.125g\]

Answer 2

And from a more mathematical standpoint...\[N(t)=N_0\frac{1}{2}^{\frac{t}{t_{1/2}}}\]Where...
N(t) is the amount of substance remaining after a time, t
N_0 is the intial amount of substance
t is the time that has surpassed
t_{1/2} is the half-life of the substance

Plugging some numbers in...\[N(1.00hr)=1.00g*\frac{1}{2}^\frac{60\min}{20.0\min}\]\[N(1.00hr)=0.125g\]

Answer 3

Thank You soooooo much!!!