IB Physics-Theme E-May 2021- an atomic electron is captured by a proton in the nucleus..Paper2

During electron capture, an atomic electron is captured by a proton in the nucleus.
(i) Write down the equation to represent this decay.
The stable nuclide thallium-2O5s (";TH) can be formed when an unstable lead (Pb) The unstable lead nuclide has a half-life of 15 x 10^6 years. A sample initially contains 2.0 micro mol of the lead nuclide.
ii) Calculate the number of thallium nuclei being formed each second 30 x 10^6 years later..
(b) The neutron number N and the proton number Z are not equal for the nuclide TH . Explain, with reference to the forces acting within the nucleus, the reason for this.
c) Thallium-TH ) can also form from successive alpha (u) and beta-minus (B-)
decays of an unstable nuclide. The decays follow the sequence alpha, beta, beta, alpha The diagram shows the position of '205 TH on a chart of neutron number against proton number.