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NEET-XII-Physics
12: Atoms
- #12The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10-40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
Ans : Radius of the first Bohr orbit is given by the relation,
Where,
∈0 = Permittivity of free space
h = Planck’s constant = 6.63 × 10-34 Js
me = Mass of an electron = 9.1 × 10-31 kg
e = Charge of an electron = 1.9 × 10-19 C
mp = Mass of a proton = 1.67 × 10-27 kg
r = Distance between the electron and the proton
Coulomb attraction between an electron and a proton is given as:
Gravitational force of attraction between an electron and a proton is given as:
Where,
G = Gravitational constant = 6.67 × 10-11 N m2/kg2
If the electrostatic (Coulomb) force and the gravitational force between an electron and a proton are equal, then we can write:
∴FG = FC
Putting the value of equation (4) in equation (1), we get:
It is known that the universe is 156 billion light years wide or 1.5 × 1027 m wide. Hence, we can conclude that the radius of the first Bohr orbit is much greater than the estimated size of the whole universe.