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  • Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is Assume that we start with 1000 38S nuclei at time t = 0

 Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

Sulphur^{38\xrightarrow[=2.48h]{half-life}}Cl^{38}\xrightarrow[=0.62h]{half-life}Ar^{38}(stable) 

Assume that we start with 1000 38S nuclei at time t = 0. The number of 38Cl is of count zero at t = 0 and will again be zero at t = \infty . At what value of t, would the number of counts be a maximum?

Answers (1)

If we consider \lambda_{1} and \lambda_{2} as the disintegration constants for S38 and Cl38 respectively.

Therefore, dN1/dt = – \lambdaN2

dN2/dt = rate of decay of Cl38 + rate of formation of Cl38

again, dN2/dt = \lambda_{2}N2+ \lambda_{1}N1

e\lambda_{2}tdN2 + \lambda_{2}N2e\lambda_{2}tdt = \lambda_{1}N0e(λ2 – \lambda_{1})dt

If we integrate the above equation,  we will get:

t = 1.65 h

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infoexpert24

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