gorovogpg

2021-12-14

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately $1.0\times {10}^{-13}$ cm. The hydrogen atom itself has a radius of approximately $52.9\pm$ . What fraction of the space within the atom is occupied by the nucleus?

kalfswors0m

Beginner2021-12-15Added 24 answers

Radius of nucleus: $1.0\times {10}^{-13}cm$

Radius of hydrogn atom:$52.9\text{}\pi cometer\text{}(\pm )$

Now, covert the given values in a single unit of measurement:

$cm\to m$

$1.0\times {10}^{-13}cm\times \frac{1m}{100cm}=1.0\times {10}^{-15}m$

$\pi cometer\to m$

$52.9\times \frac{1.0\times {10}^{-12}m}{1\pm}=5.29\times {10}^{-11}m$

Get the volume of the nucleus and the volume of the atom using:

$V}_{sphere}=\frac{4}{3}\pi {r}^{3$

For atom:

$V}_{a\to m}=\frac{4}{3}\pi {(5.29\times {10}^{-11}m)}^{3$

$V}_{a\to m}=6.2009\times {10}^{-31}{m}^{3$

For nucleus

$V}_{\nu c\le us}=\frac{4}{3}\pi {(1.0\times {10}^{-15}m)}^{3$

$V}_{\nu c\le us}=4.1888\times {10}^{-45}{m}^{3$

Now, use this frmula to find the fraction of the space within the atom is occupied by the nucleus:$X=\frac{{V}_{\nu c\le us}}{{V}_{a\to m}}$

$X=\frac{4.1888\times {10}^{-45}{m}^{3}}{6.2009\times {10}^{-31}{m}^{3}}$

$X=6.7551\times {10}^{-15}$

Radius of hydrogn atom:

Now, covert the given values in a single unit of measurement:

Get the volume of the nucleus and the volume of the atom using:

For atom:

For nucleus

Now, use this frmula to find the fraction of the space within the atom is occupied by the nucleus:

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