A) 80min
B) 120 min
C) 20 min
D) 30 min
Correct Answer: C
Solution :
The number of counts left after time t \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{t/{{T}_{1/2}}}}\] \[\therefore \] \[30=240{{\left( \frac{1}{2} \right)}^{60/{{T}_{1/2}}}}\] \[[\because \,\,t=1\,\,h=60\min ]\] or \[\frac{30}{240}={{\left( \frac{1}{2} \right)}^{60{{T}_{1/2}}}}\] or \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{60/{{T}_{1/2}}}}\] Comparing the power, we get \[\frac{60}{{{T}_{1/2}}}=3\] \[\therefore \] \[{{T}_{1/2}}=\frac{60}{3}\] or \[{{T}_{1/2}}=20\min \]
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