What is the approximate age of the ancient tree sample if specific activity of C−14 in it is 14 of the activity of newly felt trees? Half-life of C−14 is 5570 years.
A
11,140 years
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B
5570 years
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C
16,710 years
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D
2785 years
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Solution
The correct option is A 11,140 years Decay constant λ=ln2t1/2 = ln25570
Activity of the sample is given by A=λN=λN0e−λt and activity of a fresh sample will be A=λN0
Given λNλN0=14 ⇒e−λt=14 ⇒ln(1/4)=−λt ⇒t=2ln2λ This gives t=2×5570=11,140 years