A) 50 minutes
B) 100 minutes
C) 99 minutes
D) 150 minutes
Correct Answer: C
Solution :
Radioactive disintegration is a 1st order. reaction, hence, \[k=\frac{2.303}{t}\log \frac{a}{(a-x)}\] \[\therefore \] \[k=\frac{2.303}{15}\log \frac{100}{100-50}\] also, \[k=\frac{2.303}{t}\log \frac{100}{100-99}\] \[\therefore \] \[\frac{2.303}{15}\log \frac{100}{50}=\frac{2.303}{t}\log \frac{100}{l}\] \[\frac{1}{15}\log 2=\frac{1}{t}\log 100\] \[\frac{0.3010}{15}=\frac{2}{t}\] \[\therefore \] \[t=\frac{2\times 15}{0.3010}\] \[=99\] minutes
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