Calculate:

(i) the value of $a$,

$$a=\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots$$

(ii) the value of $b$.

$$b=\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots$$

(i) Identify the element from the list below that is produced by this decay:

(ii) The isotope ${}_{\mathrm{b}}^{\mathrm{a}}\mathrm{X}$ is also radioactive and undergoes $\beta$-decay. State the name of the element that is produced by this decay.

Three nuclei are represented as:

$${}_{53}^{131}\mathrm{P}{}_{54}^{131}\mathrm{Q}{}_{53}^{132}\mathrm{R}$$

State and explain which nuclei are isotopes of the same element.