Atomic radius is of order 10^-8 cm and nuclear radius is of order 10^-13. calculate what fraction of atom is occupied by nucleus?
1 Answer
Explanation:
The idea here is that you need to calculate the volume of the nucleus and compare it to the volume of the atom.
In order to be able to do that, you need to assume that both the nucleus and the atom itself are spheres.
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The volume of the nucleus will be
V_"nucleus" = 4/3pi * (10^(-13) color(white)(.)"cm")^3
The volume of the atom will be
V_"atom" = 4/3pi * (10^(-8)color(white)(.)"cm")^3
Divide the two volumes to get the fraction of the atom occupied by the nucleus
V_"nucleus"/V_"atom" = (color(red)(cancel(color(black)(4/3pi))) * (10^(-13))^3 color(red)(cancel(color(black)("cm"^3))))/(color(red)(cancel(color(black)(4/3pi))) * (10^(-8))^3 color(red)(cancel(color(black)("cm"^3))))
You will end up with
V_"nucleus"/V_"atom" = (10^(-13)/10^(-8))^3
V_"nucleus"/V_"atom" = (10^(-5))^3
V_"nucleus"/V_"atom" = 10^(-15)
This means that the nucleus occupies
