The half-life of a radioactive substance is 15 hours. If at some instance, the sample has a mass of 512 g, calculate the time it will take \(\frac{7}{8}\) of the sample to decay
A
15 hours
B
30 hours
C
45 hours
D
60 hours
Verified Correct Answer: C.
Physical Principles & Numerical Solution
Initial Mass: 512 g, Mass Decayed: \(\frac{7}{8}\) of 512 = 448g, Remaining mass = 512 - 448 = 64g
Using, N(t) = No(\(\frac{1}{2}\))\(^{\frac{T}{T1/2}}\)
\(\frac{N(t)}{No}\) = (\(\frac{1}{2}\))\(^{\frac{T}{T1/2}}\)
\(\frac{64}{512}\) = \(\frac{1}{8}\) = (\(\frac{1}{2}\))\(^{\frac{T}{15}}\)
\(\frac{1}{8}\) = (\(\frac{1}{2}\))\(^3\) = (\(\frac{1}{2}\))\(^{\frac{T}{15}}\)
equating coefficient
3 = \(\frac{T}{15}\)
T = 3 x 15 = 45hours.
Source: Myschool Past Questions Archive (Record #63378)