Let us consider for a second, that the relationship between H-atom and another particle is same as that of Sun and earth, now according to the gravitational force formula, which describe the force as an attractive force between two objects that carry a certain mass.

where

F is the gravitational force, G is the gravitational force constant, r is the distance between the 2 objects and M and m are the mass of the bigger and smaller objects on which the force is applied.

Now to find the value of the mass of the H- atoms let us check the options one by one. The first option states that the mass of H-atom is the sum of the mass of proton and electron, now ideal times this formula will do fine but due to the gravitational forces the proton and electron will be attracted towards each other and when close enough they will either run past each other or will get hit, now we want a stable mass not a volatile one. So to stop the motion of the proton and electron and placing them in one place, we need an energy to bind them in one place which is known as Binding Energy.

Now writing Binding Energy in terms of mass we get

where

is the mass generated from the neutron of the hydrogen atom, is the sum of mass of proton and electron.

Therefore, the mass of the Hydrogen Atom is