The single proton that forms the nucleus of the hydrogen

gorovogpg 2021-12-14 Answered
The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0×1013 cm. The hydrogen atom itself has a radius of approximately 52.9±. What fraction of the space within the atom is occupied by the nucleus?
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Expert Answer

kalfswors0m
Answered 2021-12-15 Author has 24 answers
Radius of nucleus: 1.0×1013cm
Radius of hydrogn atom: 52.9 πcometer (±)
Now, covert the given values in a single unit of measurement:
cmm
1.0×1013cm×1m100cm=1.0×1015m
πcometerm
52.9×1.0×1012m1±=5.29×1011m
Get the volume of the nucleus and the volume of the atom using:
Vsphere=43πr3
For atom:
Vam=43π(5.29×1011m)3
Vam=6.2009×1031m3
For nucleus
Vνcus=43π(1.0×1015m)3
Vνcus=4.1888×1045m3
Now, use this frmula to find the fraction of the space within the atom is occupied by the nucleus: X=VνcusVam
X=4.1888×1045m36.2009×1031m3
X=6.7551×1015

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