Consider radioactive decay of `A` to `B` with which further decays either to `X` or `Y`, `lambda_(1), lambda_(2)` and `lambda_(3)` are decay constant for `A` to `B` decay, `B` to `X` decay and Bto `Y` decay respectively. At `t=0`, the number of nuclei of `A,B,X` and `Y` are `N_(0), N_(0)` zero and zero respectively.
`N_(1),N_(2),N_(3)` and `N_(4)` are the number of nuclei of `A,B,X` and `Y` at any instant `t`.
The net rate of accumulation of `B` at any instant is
Consider radioactive decay of `A` to `B` with which further decays either to `X` or `Y`, `lambda_(1), lambda_(2)` and `lambda_(3)` are decay constant for `A` to `B` decay, `B` to `X` decay and Bto `Y` decay respectively. At `t=0`, the number of nuclei of `A,B,X` and `Y` are `N_(0), N_(0)` zero and zero respectively.
`N_(1),N_(2),N_(3)` and `N_(4)` are the number of nuclei of `A,B,X` and `Y` at any instant `t`.
The net rate of accumulation of `B` at any instant is
`N_(1),N_(2),N_(3)` and `N_(4)` are the number of nuclei of `A,B,X` and `Y` at any instant `t`.
The net rate of accumulation of `B` at any instant is
A
`N_(1)lambda_(1) + N_(2)lambda_(2) + N_(3)lambda_(3)`
B
`N_(1)lambda_(1) - N_(3)lambda_(2) - N_(4)lambda_(3)`
C
`N_(1)lambda_(1) - N_(2)lambda_(2) - N_(2)lambda_(3)`
D
`N_(1)lambda_(1) + N_(2)lambda_(2) - N_(3)lambda_(3)`
Text Solution
Verified by Experts
The correct Answer is:
C
Rate of production of B depends on the decaying rate (A) : `d_(N_(A))/(dt)= -lambdaN_(A)=lambdaN_(1)`
B is decaying simultaneously with two rates `d_(N_(B))/(dt)= -lambda_(2)N_(B)= -lambda_(2)N_(2)`
`d_(N_(B))/(dt) = -lambda_(3)N_(B)= -lambda_(3)N_(2)`
Number of nuclei of 'B' is `=lambda_(1)N_(1)-lambda_(2)N_(2)-lambda_(3)N_(2)`
B is decaying simultaneously with two rates `d_(N_(B))/(dt)= -lambda_(2)N_(B)= -lambda_(2)N_(2)`
`d_(N_(B))/(dt) = -lambda_(3)N_(B)= -lambda_(3)N_(2)`
Number of nuclei of 'B' is `=lambda_(1)N_(1)-lambda_(2)N_(2)-lambda_(3)N_(2)`
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