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Question
The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å : 1Å = 10−10 m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m3 of a mole of hydrogen atoms?
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Solution
Radius of hydrogen atom, r = 0.5 Å= 0.5 × 10–10 m
Volume of hydrogen atom V1 = `4/3pir^3`
`= 4/3 xx 3.14 xx (0.5 xx 10^-10)^3`
= 5.233 × 10–31 m3
According to Avogadro’s hypothesis, 1 mole of hydrogen contains
N = 6.023 × 1023 atoms.
∴ Atomic volume of 1 mole of hydrogen atoms,
V = NV1
or V = 6.023 × 1023 × 5.233 × 10–31
= 3.152 × 10–7 m3
= 3 × 10–7 m3
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