Question

The radius of atom is of the order of 1 angaston and radius of nucleus is of the order of Fermi.How many magnitudes higher is the volume of atom as compared to the volume of nucleus?

Answer 1

Let radius of nucleus be 'r'
And radius of atom be 'R'
Their shape can be supposed to be sphere
Vol Ratio = Vol of atom / Vol of nucleus
= (4/3πR³)/(4/3πr³) = (R/r)³
Now , R=10^-10m
r= 10^-15m
Volume Ratio = (10^-10/10^-15)³ = 10^125
Hence , volume of atom is 10^125 times greater than volume of nucleus

Answer 2

Radius of atom ≈ 1 Å = 1.0 × 10^(-10) m
Radius of nucleus ≈ 1 fermi = 1.0×10^(-15) m

So, ratio of radius of atom to radius of nucleus is:

1 Å/1 fermi = 10^(-10)/10^(-15) = 10^5


Now, volume = (4/3)πr³

So, ratio of volumes = (ratio of radii)³
So, ratio of volumes = (10^5)³ = 10^15


Thus, an atom has around 10^15 times more volume than a nucleus