Question

Nuclei of a radioactive element `X` are being produced at a constant rate `K` and this element decays to a stable nucleus `Y` with a decay constant `lambda` and half-life `T_(1//3)`. At the time `t=0`, there are `N_(0) `nuclei of the element `X`.
The number `N_(Y)` of nuclei of `Y` at `t=T_(1//2)` is.
A. `q(ln2)/(lambda)+(3)/(2)((q-lambdaN_(0))/(lambda))`
B. `q(ln2)/(lambda)-(3)/(2)((q-lambdaN_(0))/(lambda))`
C. `q(ln2)/(lambda)-(1)/(2)((q-lambdaN_(0))/(lambda))`
D. `q(ln2)/(lambda)+(1)/(2)((q-lambdaN_(0))/(lambda))`

Answer 1

Correct Answer - C
In the above answer sub `t=T_(1//2)`