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. What is the number N of nuclei of this element at a time t?

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1λα−α−N0λeλt

1λα−N0λe−λt

α−N0e−λt

α N01−e−λt

answer is A.

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Detailed Solution

dNdt=α−λN∫N0NdNα−λN=∫0tdtlnα−λNα−λN0−λ=tλt=lnα−λN0α−λNeλtα−λN=α−λN0αeλt−λNeλt=α−λN0N=αeλt+λN0−αλeλt=1λα+λN0e−λt−αe−λtN=1λα1−e−λt+λN0e−λt

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