Asked by star

a radioactive material is undergoin nuclear decay. After 40 minutes, 25% of the sample remains. What is the half life of the sample? Pls say the formula how to calculate it

a)10 mins
b) 20 mins
c) 40 mins
d)80 mins
e) 160 mins
Answered by DrBob222
ln(No/N) = kt.
Call No any convenient number, for example, 100, then N = 25, you know t, solve for k.
Then k = 0.693/t<sub>1/2</sub>
Solve for t<sub>1/2</sub>
Answered by star
stil i didn't get the ryt ans hw to calculate t1/2. Wats the ans ?
Answered by DrBob222
What answer did did you get. Post your work and I'll find the error.
Answered by star
m doin as k=0.693/40 and m just gettin an different ans
Answered by DrBob222
You aren't following my instructions; that's why you aren't getting the right answer.
You must find k FIRST before substituting into the half life part.
Show what you have for ln(No/N) = kt. I told you what to substitute for No and N. Substitute 40 for t.
Answered by star
m getting k as 0.03465 m doin k =0.693/40x2 so m getting k as 0.03465
Answered by DrBob222
k is correct. k = 0.03466. The rest of what you are doing is not right. 40 min is the time it took to decrease from 100 to 25. 40 min is not t<sub>1/2</sub>. Nor is 2 the half life. The half life (t<sub>1/2</sub>) is what you are looking for. I don't think your problem is chemistry; I think it is math.

So k = 0.693/t<sub>1/2</sub>
0.03466 = 0.693/t<sub>1/2</sub>. Then
t<sub>1/2</sub> = 0.693/0.03466 = 19.996 minutes which rounds to 20 min. The reason it doesn't come out exactly 20 min is because 0.693 is what I used for ln 2 and it actually is 0.69315.
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