In the nuclear emission sequence:

The mass number and atomic number of the product $Q$ respectively, are:

1. $\alpha$ emission (${}_{82}^{290}X\to Y$): $A$ decreases by 4, $Z$ decreases by 2.$Y$: $A=286,Z=80$.Positron ($e^{+}$) emission ($Y\to Z$): $A$ stays same, $Z$ decreases by 1.$Z$: $A=286,Z=79$.${\beta }^{-}$ emission ($Z\to P$): $A$ stays same, $Z$ increases by 1.$P$: $A=286,Z=80$.${\beta }^{-}$ emission ($P\to Q$): $A$ stays same, $Z$ increases by 1.$Q$: $A=286,Z=81$.Final values: $A=286,Z=81$.