Answer :

The radius of first Bohr orbit is given by the relation:

……………(1)

Where ε_{0} is the absolute permittivity of free space and is given as = 8.854 × 10^{-12} N^{-1}C^{2}m^{-2}

h is Planck’s constant and is given as 6.64 × 10^{-34} Js

e is charge on an electron and is equals to 1.6 × 10^{-19}C

m_{e} is the mass of an electron, and is equals to 9.1 × 10^{-31} Kg

m_{p} is the mass of proton and is equals to 1.67 × 10^{-27} Kg

The forces of coulomb attraction between an electron and proton is given by the relation:

Gravitational forces of attraction between an electron and proton is given by the relation

Where G is the Gravitational constant and is equal to G = 6.67 × 10^{-11} N m^{2} Kg^{2}

When coulomb force and Gravitational forces of attraction are equal

Or

…………(1)

Substituting the values of equation (1) in equation (2), we get

Substituting the values, we get

On calculating, we get

∴ r_{1}= 1.21 × 10^{29} m

Since Universe is 150billion light years wide, which concludes that the radius of first Bohr orbit is much greater than the size of the universe.

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