Atomic radius is of the order 10 ^-8 cm and nuclear radius is of the order of 10^-13cm .calculate what fraction of atom is occupied by nucleus?
Answers
Answer:
10^15
Explanation:
to find space occupied we should find the area
area =4/3 pi r^3
so area of atom/area of nucleus
=(10^-10)^3/(10^-15)^3 (since pi r^3get cancelled)
=10^15
Answer:
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.
Explanation:
volume of sphere
the volume of sphere is given by the following formula :
V= 4πr^3/3
where r is the radius of the sphere.
The volume of nucleus will be:
V nucleus=4\3 π • ( 10^-13 cm)^3
the volume of atoms will be :
V atom=4/3π•(10^-8)^3
divide the two volumes to get the fraction of the atom occupied by the nucleus:
V nucleus/ V atom
= 4/3π•(10^-13)^3 cm^3/ 4/3π• (10-8)^3 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 1/10^15 of the volume of the atom
hope it's helpful
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