A) 1080
B) 2430
C) 3240
D) 4860
Correct Answer: A
Solution :
[a] \[\lambda ={{\lambda }_{1}}+{{\lambda }_{2}}\Rightarrow \frac{1}{t}=\frac{1}{{{t}_{1}}}+\frac{1}{{{t}_{2}}}\] \[\therefore t=\frac{{{t}_{1}}{{t}_{2}}}{{{t}_{1}}+{{t}_{2}}}=\frac{810\times 1620}{810+1620}=540\operatorname{year}\] Thus it takes two half-life to remains \[\frac{1}{4}th\]of the sample, so the time \[=2\times 540=1080\operatorname{year}\]
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