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