State whether the following statements are true or false:
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.
$(i)$ In Rutherford's atomic model,the Coulombic forces between the nucleus and electrons are mathematically similar to the gravitational forces $F = G \frac{m_1 m_2}{r^2}$.
$(ii)$ Out of every $20000$ $\alpha$-particles,$\sim 10$ particles bounce back after hitting the gold foil.
$(iii)$ In Rutherford's experiment,a zinc sulfide $(ZnS)$ fluorescent screen is placed around the gold foil.
$(iv)$ Rutherford's $\alpha$-particle scattering experiment is related to the size of the atomic nucleus.
(A) $(i)$ True: Both Coulombic and gravitational forces follow the inverse-square law,$F \propto \frac{1}{r^2}$.
$(ii)$ True: Rutherford observed that very few $\alpha$-particles (about $1$ in $20000$) rebound,confirming the small size of the nucleus.
$(iii)$ True: $A$ $ZnS$ screen is used to detect the scattering of $\alpha$-particles as it produces flashes of light (scintillations) upon impact.
$(iv)$ True: The scattering pattern allowed Rutherford to estimate the size of the nucleus to be approximately $10^{-15} \ m$.
$(ii)$ True: Rutherford observed that very few $\alpha$-particles (about $1$ in $20000$) rebound,confirming the small size of the nucleus.
$(iii)$ True: $A$ $ZnS$ screen is used to detect the scattering of $\alpha$-particles as it produces flashes of light (scintillations) upon impact.
$(iv)$ True: The scattering pattern allowed Rutherford to estimate the size of the nucleus to be approximately $10^{-15} \ m$.
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