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Question
The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10−11 m from the nucleus which has a diameter of about 1.0 × 10−15 m. Assuming the hydrogen atom to be a sphere of radius 5.3 × 10−11 m, what fraction of its volume is occupied by the nucleus?
Solution
Volume of nucleus = `4/3 π"r"^3`
Volume of atom = `4/3 π"R"^3`
Fraction of volume occupied by the nucleus = `(4/3π"r"^3)/(4/3π"R"^3)`
= `(0.5 xx 10^-15)^3/(5.3 xx 10^-11)^3`
= 8.39
= 8.4 × 10−16
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