Nuclear Decay with time (half-life,initial activity/ nuclei)

In summary, the conversation was about finding the formula for the relationship between half life, initial number of unstable nuclei, and initial activity. The problem given involved calculating the initial activity and time taken for all nuclei to decay. The only formulas mentioned were for final activity and final number of nuclei, but no formula was found for the relationship between initial activity and initial number of nuclei. The idea of using a derivative to solve the problem was suggested, and the final conclusion was that A0=N0*decay constant.
  • #1
Treeps
3
0
Hi! I just keep having a hard time looking for the formula stating the relationship between half life, the initial number of unstable nuclei and the initial activity, can someone help me on that ?

To be more specific, here is a problem which can be solved using that formula:
"A substance has a half life of 100s, and starts with 1020 unstable nuclei.Calculate the initial activity, and from this work out the time taken for all of the nuclei to decay if the activity did not decrease with time"

The only formulas I could find were:
A (final activity)= A0*e-decay constant*time
N (final number of nuclei)= N0*e-decay constant*time
But nothing clearing expressing the relationship between A0 and N0
 
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  • #2
Activity is the process of nuclei "going away" (decaying) - a derivative should help.
 
  • #3
Euh is it A0=N0*decay constant ?
 
  • #5
Ok, thanks for your help !
 

FAQ: Nuclear Decay with time (half-life,initial activity/ nuclei)

1. What is nuclear decay?

Nuclear decay, also known as radioactive decay, is the process by which an unstable atomic nucleus loses energy by emitting radiation, such as alpha or beta particles, or gamma rays. This process results in the transformation of one element into another, and it continues until a stable nucleus is formed.

2. What is half-life in nuclear decay?

Half-life is the amount of time it takes for half of the original number of radioactive nuclei to decay into stable nuclei. This is a constant value for a specific radioactive isotope and can range from fractions of a second to billions of years.

3. How is half-life related to the initial activity of a sample?

The initial activity of a sample is the amount of radioactive material present at the beginning of the decay process. Half-life is inversely proportional to the initial activity, meaning that the higher the initial activity, the shorter the half-life and vice versa.

4. How is nuclear decay used in dating materials?

Nuclear decay is used in a technique called radiometric dating to determine the age of materials, such as rocks or fossils. By measuring the ratio of radioactive elements to their stable decay products, scientists can calculate the age of a material based on its known half-life.

5. What are some real-world applications of nuclear decay?

Nuclear decay has many applications, including in medicine for diagnostic imaging and cancer treatment, in energy production through nuclear power plants, and in archaeology and geology for dating materials and studying the Earth's history.

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