The half - life of a radioactive element is 9 days. What fraction of atoms has decayed in 36 days?
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Correct Answer: Option D
Explanation:
\(T _{1 / 2}=9\) days
\(No \stackrel{9 \text { days }}{\longrightarrow} \frac{ No ^{9}}{2} \stackrel{\text { days }}{\longrightarrow} \frac{ No ^{9} \text { days }}{4} \frac{ No }{8} \stackrel{9 \text { days }}{\longrightarrow} \frac{ No _{16}}{16}\)
Hence, \(\frac{N_{o}}{16}\) remained after 36 days
fraction that decayed \(=N_{0}-\frac{N_{0}}{16}\)
\(=\frac{16 N_{0}-N_{0}}{16}=\frac{15 N_{0}}{16}\)
\(T _{1 / 2}=9\) days
\(No \stackrel{9 \text { days }}{\longrightarrow} \frac{ No ^{9}}{2} \stackrel{\text { days }}{\longrightarrow} \frac{ No ^{9} \text { days }}{4} \frac{ No }{8} \stackrel{9 \text { days }}{\longrightarrow} \frac{ No _{16}}{16}\)
Hence, \(\frac{N_{o}}{16}\) remained after 36 days
fraction that decayed \(=N_{0}-\frac{N_{0}}{16}\)
\(=\frac{16 N_{0}-N_{0}}{16}=\frac{15 N_{0}}{16}\)