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Question
The ratio of the radii of hydrogen atom and its nucleus is ~ 105. Assuming the atom and the nucleus to be spherical,
- what will be the ratio of their sizes?
- If atom is represented by planet earth ‘Re ’ = 6.4 ×106 m, estimate the size of the nucleus.
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Solution
i. Volume of the sphere = `4/3 π"r"^2`
Let R be the radius of the atom and b be that of the nucleus = R = 105r
Volume of the atom = `4/3 "rR"^3`
= `4/3 π (10^5 "r")^3`
= `4/3 π"r"^3 xx 10^15`
Volume of the nucleus = `4/3 π"r"^2`
Ratio of the size of atoms to that of nucleus
= `(4/3 xx 10^15 xx π"r"^3)/(4/3 π"r"^3)`
= 1015
(ii) If the atom is represented b the planet earth (R = 6.4 × 106 m) then the radius of the nucleus would be
rn = `"R"_"n"/10^5`
rn = `(6.4 xx 10^6 "m")/10^5`
= 6.4 × 10 m
= 64 m
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