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(B) $(i)$ The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Let $R$ be the radius of the atom and $r$ be the radius of the nucleus.Given th

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$10^{15}, 64 \, m$

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(B) $(i)$ The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.Let $R$ be the radius of the atom and $r$ be the radius of the nucleus.Given the ratio $\frac{R}{r} = 10^5$,we have $R = 10^5 r$.The ratio of their volumes is $\frac{V_{atom}}{V_{nucleus}} = \frac{\frac{4}{3} \pi R^3}{\frac{4}{3} \pi r^3} = \left( \frac{R}{r} ight)^3$.Substituting the value,we get $(10^5)^3 = 10^{15}$.$(ii)$ If the atom is represented by the Earth,then $R_{atom} = R_e = 6.4 	imes 10^6 \, m$.Since $r_{nucleus} = \frac{R_{atom}}{10^5}$,we have $r_{nucleus} = \frac{6.4 	imes 10^6 \, m}{10^5} = 6.4 	imes 10^1 \, m = 64 \, m$.

The ratio of the radii of a hydrogen atom and its nucleus is $\sim 10^5$. Assuming the atom and the nucleus to be spherical,
$(i)$ What will be the ratio of their sizes (volumes)?
$(ii)$ If the atom is represented by the planet Earth $(R_e = 6.4 \times 10^6 \, m)$,estimate the size of the nucleus.

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The ratio of the radii of a hydrogen atom and its nucleus is $\sim 10^5$. Assuming the atom and the nucleus to be spherical,$(i)$ What will be the ratio of their sizes (volumes)?$(ii)$ If the atom is represented by the planet Earth $(R_e = 6.4 \times 10^6 \, m)$,estimate the size of the nucleus.