Discussion
A radio active element "X" with a half life of 2 hours decay giving a stable element "Y". After a time of \(t\) hours the ratio of atoms is 1 : 7 then, the value of
Answer: B
The value of \(t\) is 6 hours.
If the ratio of X to Y atoms is 1 : 7, then X is \(\frac{1}{8}\) of the original amount, since every decayed atom of X became an atom of Y.
\[ \begin{aligned} \left(\frac{1}{2}\right)^{n} &= \frac{1}{8} \Rightarrow n = 3 \\ t &= 3 \times 2 = 6\ \text{hours} \end{aligned} \]
14 hours treats the 7 in the ratio as the number of half-lives, and 4 hours (two half-lives) would leave \(\frac{1}{4}\), a ratio of 1 : 3.
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