Posted by **star** on Monday, May 28, 2012 at 10:38am.

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

- chemistry -
**DrBob222**, Monday, May 28, 2012 at 10:43am
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_{1/2}

Solve for t_{1/2}

- chemistry -
**star**, Monday, May 28, 2012 at 11:07am
stil i didn't get the ryt ans hw to calculate t1/2. Wats the ans ?

- chemistry -
**DrBob222**, Monday, May 28, 2012 at 11:38am
What answer did did you get. Post your work and I'll find the error.

- chemistry -
**star**, Monday, May 28, 2012 at 12:35pm
m doin as k=0.693/40 and m just gettin an different ans

- chemistry -
**DrBob222**, Monday, May 28, 2012 at 12:47pm
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.

- chemistry -
**star**, Monday, May 28, 2012 at 1:28pm
m getting k as 0.03465 m doin k =0.693/40x2 so m getting k as 0.03465

- chemistry -
**DrBob222**, Monday, May 28, 2012 at 1:41pm
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_{1/2}. Nor is 2 the half life. The half life (t_{1/2}) is what you are looking for. I don't think your problem is chemistry; I think it is math.

So k = 0.693/t_{1/2}

0.03466 = 0.693/t_{1/2}. Then

t_{1/2} = 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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