Question -
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.