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The beta^(-) activity of a sample of CO(...

The `beta^(-)` activity of a sample of `CO_(2)` prepared from a contemporary wood gave a count rate of 25.5 counts per minute (cpm) . The same mass of conditions. If the half life of `.^(14)C` is 5770 years, then the age of the statue is close to [Take `log_(1)((255)/(205))~~0.095`]

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The correct Answer is:
`a. t=821 years`,`b.` Coutn rate `=15.5 cpm`
The above magnitudes are same which means that the stability of all three atoms is same.
Initial activity `(N_(0) =25.5cpm)`
Activity after some time `(N_(1)` or `N)=20.5 cpm`
`a.` `t=(2.303)/(K)log``(N_(0))/(N_(t))`
`=(2.303xx5770year)/(0.69)log``(25.5)/(20.5)`
`=19258.4xxlog1.2439`
`=19258.4xx0.0947=1821years`
`b.` Number of counts decreases in 1821 years
`=25.5-20.5=5 cpm`
Number of counts of decrease in 4000 years
`(5)/(1821)xx4000=10 counts ~~10 counts `
Count rate of a sample which is 4000 years old
`=25.5-10=15.5cpm`
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