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Joi61 · Apr 2, 2013, 03:36 PM

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?

MacyBeee · Apr 2, 2013, 04:57 PM

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.

InfoJunkie4Life · Apr 11, 2013, 02:17 PM

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.