List of top Physics Questions on Radioactive Decay

The number of undecayed nuclei \( N \) in a sample of radioactive material as a function of time \( t \) is shown in the figure. Which of the following graphs correctly shows the relationship between \( N \) and the activity \( A \)? 

A radioactive nucleus decays as follows: \[ X \xrightarrow{\alpha} X_1 \xrightarrow{\beta^-} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4 \] If the mass number and atomic number of \( X_4 \) are 172 and 69 respectively, then the atomic number and mass number of \( X \) are
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?
A radioactive nucleus \( n_2 \) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \( n_1 \). If the initial number of both nuclei are the same, what is the ratio of the number of nuclei of \( n_2 \) to the number of nuclei of \( n_1 \), after one half-life of \( n_1 \)?
A radioactive nucleus decays as follows: \[ X \to X_1 \to X_2 \to X_3 \to X_4 \] If the mass number and atomic number of \( X_4 \) are 172 and 69 respectively, the mass number and atomic number of \( X \) are: