Question

The ratio of the radii of hydrogen atom and its nucleus is${10}^5.$ Assuming the atom and the nucleus to be spherical, how will you compare the ratio of their sizes?

• A. Volume of the sphere
• B. Surface area of sphere
• C. Volume of hemisphere
• D. Surface area of hemisphere

Answer 1

The correct option is A Volume of the sphere

The atom of hydrogen is assumed to be a sphere. Similarly, the nucleus is also assumed to be a sphere.

Volume of the sphere $=\frac{4}{3}\pi r^3$

Let R be the radius of the atom and r be that of the nucleus.

$\Rightarrow R={10}^{5}r$

Volume of the atom $=\frac{4}{3}\pi R^3=\frac{4}{3}\pi \left({10}^{5}r{)}^3\right(\because R={10}^{5}r)$

$=\frac{4}{3}\pi R^3\times {10}^{15}$

Volume of the nucleus $=\frac{4}{3}\pi r^3$

Ratio of the size of atom to that of nucleus $\frac{\frac{4}{3}\times {10}^{15}\times \pi r^3}{\frac{4}{3}\pi r^3}={10}^{15}$

Hence the correct option is A.