Question 37
The ratio of the radii of hydrogen atom and its nucleus is ∼105. 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 ′Re‘=6.4×106 m, estimate the size of the nucleus.
(a)
Volume of a sphere with radius r = 43πr3
Let R be the radius of the atom and r be that of the nucleus.
⇒ R = 105r
Volume of the atom = 43πR3
=43π(105r)3
Volume of the nucleus = 43πr3
Ratio of the size of atom to that of nucleus = 4π3R34π3r3=(105r)3r3=1015
(b) If the atom is represented by the planet earth,
Then the radius of the nucleus would be, rn=Re105
rn=6.4×106105=64 m