Half life help!

Question

How much of a 1.00 g polonium -214 sample remains after 818 microseconds? The half life of polonium -214 is 163.7 microseconds. Round to the correct number of significant figures and use units (g)

Answer 1

For me, the easiest way to solve these problems is by using the following formula:

Fraction Remaining (FR) = 0.5ⁿ where n = # of half lives that have elapsed

First, we find n: 818 usec x 1 half life/163.7 usec = 4.9969 half lives have elapsed

Now, plug this in to the formula:

F.R. = 0.5^4.9969 = 0.031317 (this is the fraction that remains)

Finally, convert this to the mass that remains (recall that 1 g = 10⁶ ug)

1.00 g x 0.031317 = 0.0313 g x 10⁶ ug/g = 3.13x10⁴ ug

Answer 2

This is an exponential decay problem.

the half-life is a period of time (t_h). After a half-life, half of a substance will remain.

So the exponential equation y = Ae^-rt is simplified, because y/A = 0.5