A) \[2.079\times {{10}^{10}}\] years
B) \[1.94\times {{10}^{9}}\] years
C) \[2\times {{10}^{15}}\] years
D) \[{{10}^{15}}\] years
Correct Answer: A
Solution :
\[x\,\,\,\,\,\,\,\,\,\to \,\,\,\,\,\,\,\,\,\,\,y\] At time \[t,\,{{n}_{0}}-x\,\,\,\,\,\,\,\,\,\,\,\,x\] \[\frac{{{n}_{0}}-x}{x}=\frac{1}{7}\] \[\Rightarrow \,{{n}_{0}}=\frac{8x}{7}\] \[\lambda =\frac{0.693}{6.93\times {{10}^{9}}}={{10}^{-10}}\] years \[t=\frac{2.303}{{{10}^{-10}}}\log \,8=\frac{2.303}{{{10}^{-10}}}\times 0.9039\] \[=2.079\times {{10}^{10}}\] years
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