NCERT Exemplar XIX — task. Science CBSE, Class 9.

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The ratio of the radii of hydrogen atom and its nucleus is ~ \(10^5\). Assuming the atom and the nucleus to be spherical,

(i). what will be the ratio of their sizes?

(ii). if atom is represented by planet earth, \(R_e = 6.4\times10^6m\), estimate the size of the nucleus.

(i). Volume of the sphere =

x π r^{3}

Where, 'x' would be

Let R be the radius of the atom and r be that of the nucleus = R = \(10^5r\)

Volume of the atom =

\frac{4}{3} π R^{3}

\begin{array}{l} = \frac{4}{3} π {{(10}^{5} r)}^{3} \\ = \frac{4}{3} π r^{3} \times 10^{15} \end{array}

Volume of the nucleus =

y \times π \times a

Where, y and a would be respectively,

Ratio of the size of the atom to that of nucleus .

\frac{\frac{4}{3} \times π r^{3} \times 10^{15}}{\frac{4}{3} \times π r^{3}}

\frac{\frac{4}{3} \times π r^{3}}{\frac{4}{3} \times π r^{3} \times 10^{15}}

= \frac{\frac{4}{3} \times π r^{3} \times 10^{5}}{\frac{2}{3} \times π r^{3}}

(ii). If the atom is represented by the planet earth (\(R_e = 6.4\times10^6m\)), then the radius of the nucleus would be

\begin{array}{l} r_{n} = \frac{R_{e}}{10^{5}} \\ = X m \end{array}

X would be .

Did you find an error?

48. NCERT Exemplar XIX