Step 1: Formula for Remaining Nuclei
We use the formula
N=N0(‌)n, where:
N= number of nuclei left
N0= starting number of nuclei
n= number of half-lives passed
Step 2: Setting Up the Ratio
The question asks for the ratio of nuclei left in
A and
B, so:
‌=‌Step 3: Simplifying the Ratio
This simplifies to:
‌=(‌)nA−nBStep 4: Finding Number of Half-lives for Each Substance
The number of half-lives
n is found by dividing total time by half-life:
For
A :
nA=‌=6For
B:nB=‌=2Step 5: Plugging In the Values
‌=(‌)6−2=(‌)4Step 6: Final Answer
(‌)4=‌ So, the ratio of the remaining nuclei in
A and
B after 9 days is
‌.