Help calculating the the activity of a radioactive sample

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SUMMARY

The discussion focuses on calculating the activity of potassium-40 (K40) in a sample of 140 grams of potassium, where 0.012% is K40. The half-life of K40 is established as 1.2 billion years. The user initially calculated the decay rate incorrectly, arriving at 3.88 * 10^-45 Bq, while the correct activity is 4200 Bq. The correct approach involves using Avogadro's number to find the number of K40 atoms and applying the decay formula R = λ * N, where λ is the decay constant derived from the half-life.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with Avogadro's number and molar mass calculations
  • Knowledge of the decay constant calculation
  • Basic proficiency in unit conversions related to mass and activity
NEXT STEPS
  • Learn how to calculate decay constants from half-lives for various isotopes
  • Study the application of Avogadro's number in determining atom counts from mass
  • Explore the concept of radioactive equilibrium and its implications in decay calculations
  • Investigate the use of decay equations in practical scenarios, such as medical applications
USEFUL FOR

This discussion is beneficial for students and professionals in nuclear physics, radiochemistry, and health physics, particularly those involved in calculating radioactive decay rates and understanding the implications of radioisotopes in biological systems.

pearlblack
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Help! calculating the the activity of a radioactive sample!

1. find activity R



2. the average 70 KF males contain 140 gram of potassium. of this 0.012% is potassium 40. the half life of potassium 40 is 1.2 billion years. so how many K40 decay per second and what is the activity of K40 in the body??



3. so my solution here is..
140g = 0.14kg
and mass of K40 = 0.14 * 0.012/100 = 1.68 * 10^-5kg
how many decay per second = (1.68*10^-5)/2 / 3600*24*365*1.2*10^12 = 2.22*10^-25kg
then i use R = \lambda * N = 0.653N/half life
= 3.88 * 10^-45 Bq
but this answer is wrong! because the correct one is 4200 Bq
so help me please! thx
 
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Okay, you've got the mass of K40 = 1.68*10^-5 kg. You need to calculate how many K40 atoms there are by multiplying by Avogadro's number and dividing by the molar mass (which is 40).
 


sorry i don't get it..
do i just
1.68*10^-5kg * 6.02*10^23/40 = 2.5284*10^17
and then sub this into the equation R=0.653N/half-life??
but the answer i get from this is 4.36*10^-3

which i think there is still something wrong in ym calculation...
 

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