The approximate radius of a H-atom is 0.05 nm, and that of proton is $1 .5 \times 10^{- 15} m .$ Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by the nucleus.

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$5 \times 10^{- 14}$

$2 \times 10^{- 16}$

$2.7 \times 10^{- 14}$

$2.7 \times 10^{- 10}$

answer is A.

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Detailed Solution

Given , radius of H-atom = 0.05nm = $0.05 \times 10^{- 9} m = 0.5 \times 10^{- 10}$ m

radius of proton = $1.5 \times 10^{- 15} m$

$\frac{V_{nucleus}}{V_{atom}} = \frac{\frac{4}{3} {πr}_{1}^{3}}{\frac{4}{3} {πr}_{2}^{3}} = {(\frac{1 .5 \times 10^{- 15}}{0 .5 \times 10^{- 10}})}^{3} = 2 .7 \times 10^{- 14}$

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