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PhysicsModern PhysicsRadioactivityMedium2 minQB

PhysicsMediumsingle choice

There are two radioactive substances A and B. Decay constant of B is twice that of A. Initially both have equal number of nuclei. After n half lives of A, rate of disintegration of both become equal. The value of n is :

Options:

Answer:

Solution:

Let $λ_{A} = λ$ , so $λ_{B} = 2 λ$ . After n half-lives of A:

$N_{A} = N_{0} 2^{- n}, t = n T_{A} = \frac{n ln 2}{λ}$

$N_{B} = N_{0} e^{- λ_{B} t} = N_{0} e^{- 2 n l n 2} = N_{0} 2^{- 2 n}$

Equal disintegration rates:

$λ N_{0} 2^{- n} = 2 λ N_{0} 2^{- 2 n} \Rightarrow 2^{n} = 2 \Rightarrow n = 1$

Hence option (A).

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:Radioactivity

⏱ 2mℹ️ Source: QB

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