A radioactive sample contains 3.25 1018 atoms of a nuclide that decays at a rate of 3.4 1013 disintegrations per 26 min.

(a) What percentage of the nuclide will have decayed after 159 d?
%

(b) How many atoms of the nuclide will remain in the sample?
atoms

(c) What is the half-life of the nuclide?
days

The equations I used were
t1/2 = ln2/k to find the half life
and N'=Ne-kt

I used the equations above and solved for part b, the number of atoms and found this to be 2.976E18 --which IS correct. I converted the 159 days into minutes, and found k by taking the rate (now in days) and dividing by the original number (N) and getting 3.836E-7 for k

I then plugged this into N*e-kt with t now in minutes and got my answer for part B. (2.976E18 atoms).

So my problem is with part 1 and 3....I thought it would be pretty straight forward, subtracting the remaining atoms from the original to get the amount that decayed. Then taking that amount, dividing it by the original to get the percent decayed. I keep getting 8.43% for this....but it's incorrect.

Finally for C, I thought I would just convert everything back to days, then take ln2/k (in days now) to get the half life...but I guess something is wrong here too. Can someone please explain how to do this? Thanks!

http://www.jiskha.com/display.cgi?id=1271457315

check my work.

To solve part a, we need to calculate the percentage of the nuclide that will have decayed after 159 days.

First, convert the given time of 159 days into minutes by multiplying it by 24 hours (since there are 24 hours in a day) and then by 60 minutes (since there are 60 minutes in an hour). This will give you the time in minutes.

159 days * 24 hours/day * 60 minutes/hour = 229,440 minutes

Next, we can use the decay rate equation you mentioned, N' = Ne^(-kt), where N' is the final number of atoms, N is the initial number of atoms, k is the decay constant, and t is the time.

Let's assume N is the original number of atoms, so N = 3.25 * 10^18.

We need to find the final number of atoms, N', after 229,440 minutes. We can rearrange the equation to solve for N':

N' = Ne^(-kt)

Substituting the given values:

N' = (3.25 * 10^18) * e^(-3.4 * 10^13 * (229,440 minutes / 26 minutes))

Now, calculate N' using a calculator. The value of N' will give us the remaining number of atoms after the given time.

To find the percentage of the nuclide that has decayed, subtract N' from N and divide the result by N, then multiply by 100 to get the percentage:

Percentage decayed = ((N - N') / N) * 100

Now, let's solve part c, which asks for the half-life of the nuclide.

The half-life (t1/2) is found using the equation t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2 and k is the decay constant.

Given that we have the value of k (3.4 * 10^13 disintegrations per 26 minutes), we can solve for t1/2 by dividing ln(2) by k.

t1/2 = ln(2) / (3.4 * 10^13 / 26)

Evaluate this expression using a calculator, and the result will give you the half-life of the nuclide in minutes.

To convert this half-life from minutes to days, divide the value by 24 hours (since there are 24 hours in a day) and then by 60 minutes (since there are 60 minutes in an hour).

This should help you solve parts a, b, and c of the problem. Let me know if you have any further questions!