| [A] Probability that a nucleus will decay is \[1-{{e}^{-\lambda t}}\] Probability that a nucleus will decay four half lives is 15/16 |
| [C] Fraction nuclei that will remain after two half lives is zero |
| [D] Fraction of nuclei that will remain after two half-lives is 1/4 |
A) A, B
B) B, C
C) B, C, D
D) A, B, D
Correct Answer: D
Solution :
\[\frac{N}{{{N}_{0}}}\,\,\equiv \,\,\] fraction of nuclei that will not decay \[1-N/No\equiv \] fraction of nuclei that will decay \[1-N/{{N}_{0}}\,\equiv \,1-{{e}^{\,-\lambda t}}\] \[\equiv \] Probability that a nucleus will decay Also, \[N/{{N}_{0}}\,\,=\,\,{{\left( \frac{1}{2} \right)}^{n}}\] Where n is the number of half lives \[\frac{N}{{{N}_{0}}}\,\,=\,\,{{\left( \frac{1}{2} \right)}^{4}}\,=\,\frac{1}{16}\] \[1-\frac{N}{{{N}_{0}}}\,\,=\,\,1-\frac{1}{16}\,=\,\frac{15}{16};\] Probability that a nucleus will decay \[\frac{N}{{{N}_{0}}}\,\,=\,\,\left( \frac{1}{2} \right){{\,}^{2}}=\,\frac{1}{4};\] fraction of nuclei that will remain after two half lives
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