The ratio of the radii of hydrogen atom and its nucleus is `~ 10^(5)`.
Assuming the atom and the nucleus to be spherical.
(a) What will be the ratio of their sizes ?
(b) If atom is represented by planet earth `'R_(e)' = 6.4 xx 10^(6)m`, estimate the size of the nucleus.

Explanation

For a sphere the volume = `(4)/(3)pir^(3)`
Let 'R' be the radius of the atom and 'r' be that of the nucleus .According to available information
R=`10^(5)r`
Volume of the atom =`(4)/(3)piR^(3)=(4)/(3)pi(10^(5)r)^(3)`
Volume of the nucleus =`(4)/(3)pir^(3)`
Ratio of the size of the atom to that of nucleus =`(4)/(3)pi10^(5)r^(3)/(4/(3)pir^(3))=10^(15)`
(ii) If the atom is represented by the planet earth with radius (Re) s given :
Radius of nucleus = `("Radius of earth")/(10^(5))=(6.4xx10^(6)x)/(10^(5))=6.4xx10 m` =64 m.