After days, the activity of a radioactive sample is . The activity reduces to after another days. What Is The initial activity of the sample in ?
Step 1. Given data
Activity reduces from to i. e. half.
days half life's
After days activity
Step 2. Concept to be used
The decays constant is the inverse of the mean lifetime (average lifetime of a radioactive particle before decay).
So, the rate equation in first order reaction is,
Here, is the initial activity and is the activity at time .
Step 3. Calculate the initial activity
Now, we will taking the number of days as time.
Substitute the values in the above expression, we get,
Equate the both equations and , we get,
Step 4. Solve by using exponential rule.
Take the exponential on both sides and solving the above equation we get,
Multiply both sides by .
Use log rules , we get,
multiply both sides by .
Take both sides of the equation to the power of , we get,
Substract from both sides, we get,
Step 5. Use zero factor principle
If then or .
Hence, the initial activity is .