Ask Me Help Desk - Lead-214

Lead-214 has a half-life of 27 minutes. If you started with 500 grams of this isotope, how many grams would you have after 54 minutes?

I'm by far no expert on this, and I may not be correct, but I took Chemistry last semester and we briefly covered this. If I took my best educated guess, I'd say that because 54/2 is 27, then you go through two half-life reductions. Not saying that it would all be gone, but it would be divided by 2 twice. Therefore, you'd do 500/2=250; then 250/2=125. So 125g should be your final answer.

Although MacyBeee is correct it is important to understand the following equation. This will make it possible to solve half life problems that do not have such friendly numbers.

$N(t) = N_0 \left(\frac {1}{2}\right)^{t/t_{1/2}}$

$N(t)$ Is the remaining quantity.

$N_0$ Is the initial quantity.

$t_1/2$ Is the half life.

$t$ Is the time the initial quantity is to be decayed.

Relative to your problem it would look something like this:

$N(t) = 500 \left(\frac {1}{2}\right)^{54/27}$

54/27 is 2.
1/2 squared is 1/4.
1/4 of 500 is 125... your answer.

You may also use this equation to solve for initial quantity or time.