of any given amount of the substance disintegrates in 40 minutes?
A) 20 min
B) 10 min
C) 13 min 32 s
D) 160 min
Correct Answer: C
Solution :
\[\operatorname{Given} initial mass =a\] Mass left after time \[\operatorname{t} =x= 0.875\,a\] \[t=40\,\,min\] \[k=\frac{2.303}{t}\log \frac{a}{a-x}=\frac{2.303}{40}\log \frac{a}{a-0.875\,a}\] \[=\,\frac{2.303}{40}\log \,\,8=0.052\,\,{{\min }^{-1}}\] \[{{t}_{1/2}}=\frac{0.693}{k}=\frac{0.693}{0.052}=13\,\,\min \,\,32\,s\]
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