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.

Answers (1)

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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