Nuclear Chemistry - Result Question 9
####12. One microgram of radioactive sodium $ _11^{24} Na$ with a half-life of 15 hours was injected into a living system for a bio-assay. How long will it take for the radioactive subtance to fall up to $25 %$ of the initial value?
[1996]
(a) 60 hours
(b) 22.5 hours
(c) 375 hours
(d) 30 hours
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Solution:
- (d) $\quad N=N_0(\frac{1}{2})^{n}$; here, $N=\frac{N_0}{4}$
$\frac{N_0}{4}=N_0(\frac{1}{2})^{n} \Rightarrow(\frac{1}{2})^{n}=(\frac{1}{2})^{2} \Rightarrow n=2$
Total time $(T)=n \times t _{1 / 2}=2 \times 15=30 hrs$
