In 24 days a radioactive isotope decreases in mass from 128g to 2g. What is the half-life of the radioactive material?
A
2.54 days
B
4.00 days
C
4.80 days
D
6.00 days
E
8.00 days
Verified Correct Answer: B.
Physical Principles & Numerical Solution
N = N\(_o\)(\(\frac{1}{2}\))\(^{\frac{t}{T_{\frac{1}{2}}}}\)
N = 2g, N\(_o\) = 128g, t =24days and \(T_{\frac{1}{2}}\) = ?
2 = 128(\(\frac{1}{2}\))\(^{\frac{24}{T_{\frac{1}{2}}}}\)
\(\frac{2}{128}\) = (\(\frac{1}{2}\))\(^{\frac{24}{T_{\frac{1}{2}}}}\)
\(\frac{1}{64}\) = (\(\frac{1}{2}\))\(^{\frac{24}{T_{\frac{1}{2}}}}\)
(\(\frac{1}{2}\))\(^6\) = (\(\frac{1}{2}\))\(^{\frac{24}{T_{\frac{1}{2}}}}\)
6 = \(\frac{24}{T_{\frac{1}{2}}}\)
\(T_{\frac{1}{2}}\) = \(\frac{24}{6}\) = 4 days.
Source: Official Exam / Past Question Archive