The 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.

Explanation

To estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction, we can follow these steps:

### Step 1: Understand the Forces
In a hydrogen atom, the electron and proton experience a gravitational force instead of the usual Coulomb force. We need to derive the radius of the first Bohr orbit using gravitational attraction.

### Step 2: Use the Bohr Model
According to the Bohr model, the centripetal force required to keep the electron in orbit is provided by the gravitational force between the electron and proton. The gravitational force \( F_g \) is given by:

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