A) 1200s, 0.173 disintegration /s
B) 1000 s, 0.173 disintegration /s
C) 1000 s, 1.173 disintegration/s
D) 1200 s, 1.173 disintegration /s
Correct Answer: A
Solution :
Initial number of molecules \[{{N}_{0}}=600\] Disintegrated number of molecules = 450 So, undisintegrated number of molecules \[N=600-450=150\] \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\therefore \] \[150=600{{\left( \frac{1}{2} \right)}^{\frac{t}{{{T}_{1/2}}}}}\] Or \[\frac{150}{600}={{\left( \frac{1}{2} \right)}^{t/600}}\] Or \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{t/600}}\] Or \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{t/600}}\] \[\therefore \] \[\frac{t}{600}=2\] or \[t=600\times 2=1200\text{ }s\] Now, rate of disintegration, \[R=-\frac{dN}{dt}=\lambda N\] \[=\frac{0.693}{{{T}_{1/2}}}\times N\] \[=\frac{0.693}{600}\times 150=0.173\] disintegration/s.
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