Ncert Exercises & Solutions

20. The radius of the atom is of the order of 1 $\overset{o}{A}$ and the radius of a nucleus is of the order of fermi. How many magnitudes higher is the volume of an atom as compared to the volume of the nucleus?

Hint: Consider an atom and a nucleus as spheres.

Step 1: Find the volume of the atom and the nucleus.

\begin{array}{l} Radius of atom = 1 \overset{o}{A} = 10^{- 10} m \\ Radius of nucleus = 1 fermi = 10^{- 15} m \\ Volúme of atom = V_{A} = \frac{4}{3} {πR}_{A}^{3} \\ Volume of nucleus V_{N} = \frac{4}{3} {πR}_{N}^{3} \\ Step 2 : Find the ratio . \\ \frac{V_{A}}{V_{N}} = \frac{\frac{4}{3} {πR}_{A}^{3}}{\frac{4}{3} {πR}_{N}^{3}} = {(\frac{R_{A}}{R_{N}})}^{3} = {(\frac{10^{- 10}}{10^{- 15}})}^{3} = 10^{15} \end{array}

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