In a sample of 86 211 Rn nuclei, 25 percent decay by α -decay to 84 207 Po and the rest decay by electron capture to 85 211 At . What is the ratio of the mean life for α -decay, τ α , to the m

Question

In a sample of 86 211 ​ Rn nuclei, 25 percent decay by α -decay to 84 207 ​ Po and the rest decay by electron capture to 85 211 ​ At . What is the ratio of the mean life for α -decay, τ α ​ , to the mean life for electron capture, τ β ​ ​ ?

TestHub · Accepted Answer

​ P α − d ec a y ​ = 0.25 α λ α ​ = T α ​ ln 2 ​ P β ​ = 0.75 α λ β ​ = T β ​ ln 2 ​ ⇒ 3 1 ​ = T α ​ T β ​ ​ ⇒ T β ​ T α ​ ​ = 3 ​

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JEE Advanced (2028)