$[$Maximum mark $7]$

$21M2SL$ T$22\mathrm{.}4$

During electron capture, an atomic electron is captured by a proton in the nucleus. The stable nudide thallium$-205{(}_{81}^{205}Tl)$ can be formed when an unstable lead $(Pb$ nuclide captures an electron.

$($a$)$ Write down the equation to represent this decay.

$($b$)$ The neutron number $N$ and the proton number $l$ are not equal for the nuclide ${?}^{205}ML.$ Explain, with reference to the forces acting within the nucleus, the reason for this.

$($c$)$ Thallium$-205(\frac{205}{81}Tl)$ can also form from successive alpha $($a$)$ and beta$-$minus $()$ decays of an unstable nuclide. The decays follow the sequence $a{}^{-1}{}^{-}a.$ The diagram shows the position of ${?}^{205}$ Tl on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N I and? that occuras the ${?}^{205}$ II forms from the unstable nudide.