State whether the following statements are true or false:
$(i)$ Faraday's electrolysis experiments and cathode ray discharge tube experiments prove that protons are located in the nucleus of the atom,while electrons are located outside the nucleus.
$(ii)$ In the year $1887$,Goldstein discovered the proton.
$(iii)$ In the year $1932$,the neutron was discovered by Chadwick.
$(iv)$ The first atomic model was proposed by Thomson.

(A) $(i)$ False. Faraday's experiments and cathode ray tubes do not directly prove the location of protons in the nucleus; this was established by Rutherford's alpha-particle scattering experiment.
$(ii)$ False. Goldstein discovered anode rays (canal rays) in $1886$,which were later identified as protons,but the discovery is generally attributed to the $1886$ experiments.
$(iii)$ True. James Chadwick discovered the neutron in $1932$.
$(iv)$ True. $J$.$J$. Thomson proposed the first atomic model (Plum Pudding Model) in $1898$.