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The nuclei of a certain radioactive element are produced at a constant rate of  α per second. This element has a decay constant λ . Initially N0  nuclei of the element are present.

If in the above question α=2λN0  calculate the number of nuclei left in the element after one half life period of the element.

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a
N02
b
3N02
c
2N03
d
N04

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detailed solution

Correct option is B

λt=ln 2λN0−λN02λN0−λNλln 2λ=ln λN02λN0−λN2=λN02λN0−λN4λN0−2λN=λN0N=32N0

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