Beryllium-11 decomposes into boron-11 with a half-life of 13.8 seconds. How long will it take 2400 g of beryllium-11 to decompose into 75 g of beryllium-11?

Question

whpalmer4 · Answer

After 1 half-life, 1/2 of the substance will have decayed.  We want to find out how many half-lives need to pass (each one halving the amount remaining) to decay 2400 g to 75 g.

$$\frac{75}{2400} = \frac{1}{2^{n}}$$ where n is the number of half-lives.  Cross-multiply and solve for n.

anonymous · Answer

start with 1200

one half life 

600

two half lifes

300

three half lifes

150

four half lifes

75

it takes 13.8 second per half lives, and you have 4 of them.

whpalmer4 · Answer

Um, you start with 2400 :-)

whpalmer4 · Answer

When you've settled on the number of half-lives, multiply by the length of a half-life to get the total duration.

anonymous · Answer

your right i misread it.

whpalmer4 · Answer

Bonus question: about how many half-lives have to pass to get to 1% of the original concentration?  

The shorter the half-life, the more radioactive the substance is.  Beryllium-11 is pretty hot!  The good news is that it doesn't stick around very long...  Wouldn't want to hold that slug of Be in your hand while it decayed into B.