# The ratio of volume of atom to volume of nucleus is

To find the ratio of the volume of an atom to the volume of the nucleus.

Let us consider

The radius of the atom (r1) = 10-10

The radius of the nucleus (r2) = 10-15

Let us take the volume of the atom to the volume of the nucleus, then we get

$\frac{Volume\, of\, atom }{Volume\, of\, nucleus} =\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}$

⇒ $\frac{\left ( 10^{-10} \right )^{3}}{\left ( 10^{-15} \right )^{3}}$

⇒ $\frac{10^{-30}}{10^{-45}} = 10^{\left ( -30+45 \right )}$

⇒ $10^{15}$

Hence the ration of the volume of an atom to the volume of the nucleus is 1015.

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