The count rate of an alpha-particle source is 400 per minute. If the half-life of the source is 5 days, what would be the count rate per minute after 15 days?
A
20
B
25
C
50
D
200
E
400
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Initial count rate N\(_o\) = 400 per minute, Half-life\(T_{\frac{1}{2}}\) = 5 days, T = 15days, N (count after 15 days) = ?
Using: N = N\(_o\)(\(\frac{1}{2}\))\(^{\frac{T}{T_{\frac{1}{2}}}}\)
N = 400 x (\(\frac{1}{2}\))\(^{\frac{15}{5}}\)
N = 400 x \(\frac{1}{2}\)\(^3\) = 400 x \(\frac{1}{8}\) = \(\frac{400}{8}\) = 50.
Source: Myschool Past Questions Archive (Record #25258)