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Equal amounts of two samples of carbon w...

Equal amounts of two samples of carbon were burnt and the radioactivities of`CO_2` formed were measured. The activitied were 2100and 1400 counts per week respectively. What will be the age difference of the sample. [ `t_(1//2)` for`C^(14) = 560`0 years ]

A

2002 years

B

2345 years

C

4250 years

D

3343 years

Text Solution

Verified by Experts

The correct Answer is:
D
`t_(1//2) = 5600` years
Decay constant , `lambda = (0.693)/(t_(1//2)) = (0.693)/(5600) = 1.24 xx 10^(-4) "year"^(-1)`
For first sample : `(N_0)/(N) = ("Number of counts per week of carbon initially")/("number of counts per week of carbon finally")`
`= (N_0)/(2100) " ".......(i)`
For second sample : `(N_0)/(N) = (N_0)/(1400) " " .......(ii)`
The age difference of the sample :
`t = (2.303)/(lambda) ["log" (N_0)/(1400) - "log" (N_0)/(2100)]`
`= (2.303)/(1.24 xx 10^(-4))["log" N_0 - "log" 1400 - "log" N_0 + log 2100]`
`= (2.303)/(1.24 xx 10^(-4)) [log 2100 - log 1400]`
`= (2.303)/(1.24 xx 10^(-4)) [3.32 - 3.14]`
`= t = (2.303)/(1.24 xx 10^(-4)) xx 0.18 = 3343.06` years
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