# The ratio of the radii of hydrogen atom and its nucleus is $\sim 10^{5}$. Assuming the atom and the nucleus to be spherical. (a) What will be the ratio of their sizes ? (b) If atom is represented by planet earth $'R_{e}'=6.4 \times 10^{6} m$, estimate the size of the nucleus.

Given is the ratio of the radii of hydrogen atom and its nucleus is $\sim 10^{5}$.

And assuming the atom and the nucleus to be spherical.

(i) Sphere of volume $=\frac{4}{3}\pi r^{3}$

Let ''R'' be the radius of the atom and ''r'' be the radius of nucleus,

Therefore, $R=10^{5}r$

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

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

Ratio of size of the atom to that of nucleus$=10^{15}$

(ii) If the atom is represented by planet earth (Radius Re)

Radius of nucleus $=\frac{\text {Radius of Earth}}{10^{5}}=\frac{6.4\times 10^{6}}{10^{5}}m=64m$

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