Question

If the half-life of a 20.0 g sample is known to be 24 minutes, how long will it take for only 5.0 grams of the sample to remain?

Answer 1

1/2 life * 20 g = 24 min

so how much is 5 gms of it

Answer 2

half life of 20 gm means 20/2 i guess i.e = 10 gms.
so 10 gms = 20 min
1gms = 20/10

now 5gms = (20/10)* 5
i got confused with half life..

Answer 3

\[A(t) = A_0 (2)^{-t/24}\]is the formula for the amount remaining at time \(t\) (in minutes) if the initial amount is \(A_0\).

Answer 4

The half-life is the time it takes for half of the quantity to decay into something else. After 1 half-life, you'll have 1/2 the initial quantity. After 2 half-lives, you'll have 1/2*1/2 = 1/4 the initial quantity, and so on. If you have an easy problem like this one, where measurements are taking at multiples of the half-life, you don't need to use the exponential formula I provided. However, if you wanted to find the amount remaining after a different amount of time, or find the exact time to reach a different quantity, the formula is the way to go. For example, if you wanted to find how long it takes to decay down to 1% of the initial quantity:

\[A(t) = 0.01A_0 = A_0(2)^{-t/24}\]\[0.01 = 2^{-t/24}\]\[\log_2(0.01) = -t/24\]\[t = -24\log_2 (0.01) = -24\frac{\log_{10}(0.01)}{\log_{10}2} \approx -24\frac{(-2)}{0.30103} = 159.5\text{ min}\]