exponents questions?

Question

. a) How long would it take for a 1 g sample of Polonium 210 to lose 3/4 of its mass if it's half-life is 140 days?

b) How long will it take before it loses all but 1/128 of its inital mass?

Answers a= 280 b= 980 days

2. At the end of 15 days, one eight of a raidoactive sample of Bismuth 210 remains. What is the half-life of this element?

answer 5 days

can't get these answers

Answer 1

do your own homework, my friend :)

all the best ;)

Answer 2

Half life is defined as the time period in which a quantity of radioactive material will lose half its mass by way of radioactivity.

If Polonium 210 has a half-life of 140 days , it means that if you start with 1 gram of Polonium , after 140 days , you will have only 0.5 grams left. After another 140 days , you will be left with half of 0.5 grams i.e. 0.25 grams. So in 280 days , 3/4 grams of Polonium would have decayed through radioactivity.

If you go through the pattern , you will see that 1/2 is lost in one half life ; 1/2 + 1/4 is lost after 2 half-lives. Thus to lose 127/128 ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 ) will take 7 half-lives = 140 * 7 days = 980 days.

2. If 1/8 of the original sample has to remain , it means 7/8 is lost. This can come through the addition of 1/2 + 1/4 + 1/8. This means 3 half-lives. Equating this to 15 days , we see that 1 half-life is 5 days.

Answer 3

The general formula you want to use for these is:

end = start (0.5)^(3 of changes)

So,
1a)
Remember that "losing 3/4" is the same as "having 0.25"
So,
0.25 = 1(0.5)^(days/140)
and solve from there using logs

all the rest are done the same way.

Answer 4

see your earlier posting...