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A radioactive sample disintegrates via two independent decay processes having half lives \({\mathrm{T}}_{1/2}^{(1)}\) an…

Q1

A radioactive sample disintegrates via two independent decay processes having half lives \({\mathrm{T}}_{1/2}^{(1)}\) and \({\mathrm{T}}_{1/2}^{(2)}\) respectively. The effective half-life, \({\mathrm{T}}_{1/2}\) of the nuclei is:

[JEE Main 2021, 18 Mar (Shift 1)]

a

\({\mathrm{T}}_{1/2}=\frac{{\mathrm{T}}_{1/2}^{(1)}{\mathrm{T}}_{1/2}^{(2)}}{{\mathrm{T}}_{1/2}^{(1)}+{\mathrm{T}}_{1/2}^{(2)}}\)

b

\({\mathrm{T}}_{1/2}={\mathrm{T}}_{1/2}^{(1)}+{\mathrm{T}}_{1/2}^{(2)}\)

c

\({\mathrm{T}}_{1/2}=\frac{{\mathrm{T}}_{1/2}^{(1)}+{\mathrm{T}}_{1/2}^{2}}{{\mathrm{T}}_{1/2}^{(1)}-{\mathrm{T}}_{1/2}^{(2)}}\)

d

None of these

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