\( {}_{82}^{290}\text{X} \xrightarrow{\alpha} \text{Y} \xrightarrow{e^+} \text{Z} \xrightarrow{\beta^-} \text{P} \xrightarrow{e^-} \text{Q} \) In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are:

1) \( \alpha \)-decay: \( A = 290 - 4 = 286, Z = 82 - 2 = 80 \). 2) Positron emission (\( e^+ \)): \( A = 286, Z = 80 - 1 = 79 \). 3) Beta minus emission (\( \beta^- \)): \( A = 286, Z = 79 + 1 = 80 \). 4) Electron emission (\( e^- \)): \( A = 286, Z = 80 + 1 = 81 \).\nThus, for product Q, mass number = 286 and atomic number = 81.