Question:
At a given instant, there are $25\%$ undecayed radioactive nuclei in a sample. After $10$ seconds the number of undecayed nuclei reduces to $12.5\%$, the mean life of the nuclei is
At a given instant, there are $25\%$ undecayed radioactive nuclei in a sample. After $10$ seconds the number of undecayed nuclei reduces to $12.5\%$, the mean life of the nuclei is
Updated On: Jul 6, 2022
- $10.21\,s$
- $14.43\,s$
- $5.31\,s$
- $7.43 \,s$
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The Correct Option is B
Solution and Explanation
As the number of undecayed nuclei decreases from $25 \%$ to $12.5\%$ in $10\, s$, it shows that the half life of the sample is $10\, s$, i.e. $T_{1/2}=10\,s$
Decay constant, $\lambda=\frac{0.6931}{T_{1 /2}}=\frac{0.6931}{10\,s}$
Mean life, $\tau=\frac{1}{\lambda}=\frac{10\,s}{0.6931}=14.43\,s$
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Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
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Following are the terms related to nucleus:
- Atomic Number
- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit