Answer:
For 12000 years it is 1.1 × 10¹²
For 12 hours it is 9.66 × 10¹⁸
For 12 minutes it is 5.8 × 10 ²⁰
For 12 seconds it will be 3.48 × 10 ²²
Explanation:
We know that in radioactive disintegration,
Activity = [tex]$\lambda N$[/tex]
Where, [tex]$\lambda =decay constant[/tex]
N is the number of nuclei available for decay, Here we have
[tex]$N=6.02\times {{10}^{23}}$[/tex] atoms for decay, So
[tex]$\lambda =\frac{\ln 2}{{{t}_{{\scriptstyle{}^{1}/{}_{2}}}}}$[/tex]
(a) Total activity = [tex]$\lambda N$[/tex] [tex]$=\frac{0.693}{12000\times 31536000}\times 6.023\times {{10}^{23}}decays/\sec $[/tex]
[tex]$=1.1\times {{10}^{12}}$[/tex]
(b) Total activity = [tex]$\lambda N$[/tex] [tex]$=\frac{0.693}{12\times 3600}\times 6.023\times {{10}^{23}}decays/\sec $[/tex]
[tex]$=9.66\times {{10}^{18}}$[/tex]
(c) Total activity = [tex]$\lambda N$[/tex] [tex]$=\frac{0.693}{12\times 60}\times 6.023\times {{10}^{23}}decays/\sec $[/tex]
[tex]$=5.8\times {{10}^{20}}$[/tex]
(d) Total activity = [tex]$\lambda N$[/tex] [tex]$=\frac{0.693}{12}\times 6.023\times {{10}^{23}}decays/\sec $[/tex]
[tex]$=3.48\times {{10}^{22}}$[/tex]
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