A nucleus \( {}^{238}_{92}\mathrm{X} \) emits one alpha particle and then one beta particle (electron). The product nucleus will have
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Atomic number = 91, Mass number = 234
An alpha particle \( {}^{4}_{2}\mathrm{He} \) carries away 4 units of mass number and 2 units of charge. In beta-minus decay a neutron changes into a proton and an electron is emitted, so \( Z \) rises by 1 and \( A \) does not change.
\( \displaystyle {}^{238}_{92}\mathrm{X} \rightarrow {}^{234}_{90}\mathrm{Y} + {}^{4}_{2}\mathrm{He} \)
\( \displaystyle {}^{234}_{90}\mathrm{Y} \rightarrow {}^{234}_{91}\mathrm{Z} + e^{-} + \bar{\nu} \)
The product has atomic number 91 and mass number 234.