The half life of a radioactive substance is 14 days. If 48g of this substance is stored, after how many days will 1.5g of the original substance remain?
A
84 days
B
70 days
C
56 days
D
40 days
Verified Correct Answer: B.
Physical Principles & Numerical Solution
Using N = N\(_o\)\((\frac{1}{2})^n\)
N\(_o\) = 48g, N =1.5g and n = number of half-lives
1.5 = 48\((\frac{1}{2})^n\)
\(\frac{1.5}{48}\) = \(\frac{1}{32}\) = (\(\frac{1}{2})^5\) = \((\frac{1}{2})^n\)
n = 5 (same base, equate power)
Total time = n x t\(_{\frac{1}{2}}\) = 5 x 14 = 70 days
Therefore, 1.5g will remain after 70 days.
Source: Myschool Past Questions Archive (Record #33851)