First slide
Kinetics of nuclear reactions or nuclear chemistry
Question

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.

Difficult
Solution

λt=ln2λN0λN02λN0λN

λln2λ=lnλN02λN0λN

2=λN02λN0λN

4λN02λN=λN0

N=32N0

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