Radioactive Decay: Calculate % Decayed, Atoms Remaining, Half-Life

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SUMMARY

The discussion focuses on calculating radioactive decay parameters for a sample containing 3.25 x 1018 atoms of a nuclide with a decay rate of 3.4 x 1013 disintegrations per 26 minutes. The correct calculations yield 8.46% decay after 159 days and 2.976 x 1018 remaining atoms. The half-life is determined using the formula t1/2 = ln2/k, where k is derived from the decay rate. The user encountered arithmetic errors while calculating the percentage decayed and the half-life.

PREREQUISITES
  • Understanding of radioactive decay concepts
  • Familiarity with the decay constant (k) and its calculation
  • Knowledge of logarithmic functions, specifically natural logarithm (ln)
  • Ability to convert time units (days to minutes) for calculations
NEXT STEPS
  • Learn how to derive the decay constant (k) from decay rates
  • Study the application of the exponential decay formula N' = N e-kt
  • Explore the concept of half-life in various radioactive materials
  • Practice solving problems involving radioactive decay with different initial conditions
USEFUL FOR

Students in physics or chemistry, educators teaching radioactive decay, and anyone interested in understanding the principles of nuclear physics and decay calculations.

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Homework Statement



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

Homework Equations



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

The Attempt at a Solution



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 hte remaining atoms from the original to get the amount that decayed. Then taking that amount, dividing it by the original to get hte 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!
 
Physics news on Phys.org
Your methods are correct. You could be making errors in arithmetic. For what it's worth, I get 8.46% for part (a).
 

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