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  4. The mass numbers of nuclei A and B are respectively 135 and 5. The ratio of their radii is

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Q. The mass numbers of nuclei A and B are respectively 135 and 5. The ratio of their radii is

Rajasthan PMTRajasthan PMT 2011

Solution:

We know that $ m=\frac{4}{3}\pi {{r}^{3}}d $ $ \therefore $ $ m\propto {{r}^{3}} $ $ r\propto {{(m)}^{1/3}} $ Here $ \frac{{{r}_{A}}}{{{r}_{B}}}={{\left( \frac{{{m}_{A}}}{{{m}_{B}}} \right)}^{1/3}} $ $ \frac{{{r}_{A}}}{{{r}_{B}}}={{\left( \frac{135}{5} \right)}^{1/3}} $ $ \frac{{{r}_{A}}}{{{r}_{B}}}={{\left( 27 \right)}^{1/3}} $ $ \frac{{{r}_{A}}}{{{r}_{B}}}=\frac{3}{1} $