State, using nuclide notation, the symbol for:

(i) a cobalt (atomic symbol $Co$) nucleus which has nucleon number 60 and proton number 27,

(ii) a gold (atomic symbol $Au$) nucleus which contains 79 protons and 118 neutrons.

(i) A nucleus of polonium-210 (${}_{84}^{210}Po$) decays to a lead (atomic symbol $Pb$) nucleus by the emission of an $\alpha$-particle. Write down the nuclear equation that represents this radioactive decay.

(ii) The half-life of polonium-210 is 138 days. A sample contains $6.4\times 10^{11}$ atoms of polonium-210. Predict the number of polonium-210 atoms in the sample that decay in 414 days.