A) \[\frac{1}{2}\sec \]
B) \[1\,\sec \]
C) \[\frac{3}{8}\sec \]
D) \[\frac{3}{4}\sec \]
Correct Answer: C
Solution :
If \[\frac{3}{4}\] part decays If means \[\frac{1}{4}\]part remain undecayed Now from the formula \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{n}}\] \[{{\left( \frac{1}{2} \right)}^{2.}}={{\left( \frac{1}{2} \right)}^{n}}\] So, \[n=2\] \[n\times {{T}_{1/2}}=t\] \[2\times {{T}_{1/2}}=\frac{3}{4}\] Thus \[{{T}_{1/2}}=\frac{3}{8}\sec \]
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