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Question
The unit length convenient on the atomic scale is known as an angstrom and is denoted by ˚A:(1˚A=10−10m). The size of a hydrogen atom is about 0.5 ˚A. 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 = (4/3) π r3
= (4/3) × (22/7) × (0.5 × 10-10)3
= 0.524 × 10-30 m3
1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.
∴ Volume of 1 mole of hydrogen atom = 6.023 × 1023 × 0.524 × 10–30
= 3.16 × 10–7 m3
Volume of hydrogen atom = (4/3) π r3
= (4/3) × (22/7) × (0.5 × 10-10)3
= 0.524 × 10-30 m3
1 mole of hydrogen contains 6.023 × 1023 hydrogen atoms.
∴ Volume of 1 mole of hydrogen atom = 6.023 × 1023 × 0.524 × 10–30
= 3.16 × 10–7 m3
∴ Volume of 1 mole of hydrogen atom = 6.023 × 1023 × 0.524 × 10–30
= 3.16 × 10–7 m3
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3
). Why is this ratio so large?