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Question -

The gravitational attractionbetween electron and proton in a hydrogen atom is weaker than the coulombattraction by a factor of about 10−40. An alternative way of lookingat this fact is to estimate the radius of the first Bohr orbit of a hydrogenatom if the electron and proton were bound by gravitational attraction. Youwill find the answer interesting.



Answer -

Radius of the first Bohr orbit isgiven 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

Coulombattraction between an electron and a proton is given as: 

Gravitational force of attractionbetween 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 is156 billion light years wide or 1.5 × 1027 m wide. Hence, wecan conclude that the radius of the first Bohr orbit is much greater than theestimated size of the whole universe.

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