nuclear chemistry

Question

It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. What is the half-life of radium-230?

Answer 1

One easy way to do calculations involving 1st order decay is to use the following expression:

FR = 0.5ⁿ

FR = fraction remaining = 0.25 mg / 2.00 mg = 0.125

n = number of half lives that have elapsed = ?

0.125 = 0.5ⁿ

log 0.125 = n log 0.5

-0.903 = -0.301 n

n = 3 half lives

Since this is equivalent to 4 h 39 min, we can find the half life in minutes as follows:

4h x 60 min/h = 240 min = 39 min = 279 min

3 half lives / 279 min = 1 half life / x min

x = 93 minutes = half life of radium-230