A radioactive material P first decays into Q and then Q decays to non-radioactive material R. Which of the following figure represents time dependent mass of P, Q and R?

### Related Formula N = N_0 e^-lambda t$$N = N_0 e^{-\lambda t}$$ where lambda$\lambda$ is the decay constant. ### Core Logic Initially, only material P is present, so its mass decreases exponentially from a maximum value to zero. Material Q is formed from P and then decays into R, so its mass initially increases from zero, reaches a maximum, and then decreases to zero. Material R is stable and accumulated over time, so its mass increases continuously from zero and levels off at a maximum value equal to the initial mass of P. ### Step 1: Graphical Identification Looking at the options, option (2) correctly depicts the exponential decay of P, the transient rise and fall of Q, and the continuous growth of R to a stable value.

### Pattern Recognition For sequential decay P rightarrow Q rightarrow R$P \rightarrow Q \rightarrow R$, parent P$P$ always starts at max and drops to 0. Intermediate Q$Q$ starts at 0, peaks, and returns to 0. Final stable product R$R$ starts at 0 and grows asymptotically to max value. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Nuclei