Question:
If you inject a mouse with radioactive material of current activity of 256 Bq, what will be the activity after completion of 6 half-lives?
- 4 Bq
- 8 Bq
- 16 Bq
- 24 Bq
Rephrasing the Question:
How do you calculate radioactive half-life?
Answer:
4 Bq (option 1)
Explanation:
A half-life is the time it takes for a radioactive material to degrade to half its original amount. So, if you start off with 100 Bq worth of material, after one half-life, you will have 50 Bq left. After 2 half-lives, you will have 25 Bq left.
The formal equation for this is:
N(t) = N0 (1/2)n
where N(t) is the quantity of substance remaining, N0 is the initial quantity of the substance, and n is the number of half-lives elapsed.
But the easiest – and quickest! – way to answer these questions is to just calculate the quantity step-by-step.
So for this question, we would do this:
At the beginning (after 0 half-lives) = 256 Bq
After 1 half-life = previous amount / 2 = 256 Bq / 2 = 128 Bq
After 2 half-lives = previous / 2 = 128 Bq / 2 = 64 Bq
After 3 half-lives = previous / 2 = 64 Bq / 2 = 32 Bq
After 4 half-lives = previous / 2 = 32 Bq / 2 = 16 Bq
After 5 half-lives = previous / 2 = 16 Bq / 2 = 8 Bq
After 6 half-lives = previous / 2 = 8 Bq /2 = 4 Bq
Therefore, after 6 half-lives there will be 4 Bq remaining.
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