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Home » The gravitational attraction amongst proton and electron in a hydrogen atom is weaker than the coulomb attraction by a component of around 10−40. Another option method for taking a gander at this case is to assess the span of the first Bohr circle of a hydrogen particle if the electron and proton were bound by gravitational attraction. You will discover the appropriate response fascinating.
The gravitational attraction amongst proton and electron in a hydrogen atom is weaker than the coulomb attraction by a component of around 10−40. Another option method for taking a gander at this case is to assess the span of the first Bohr circle of a hydrogen particle if the electron and proton were bound by gravitational attraction. You will discover the appropriate response fascinating.
CBSE | Class 12 | NCERT | Nuclei | Physics
The gravitational attraction amongst proton and electron in a hydrogen atom is weaker than the coulomb attraction by a component of around 10−40. Another option method for taking a gander at this case is to assess the span of the first Bohr circle of a hydrogen particle if the electron and proton were bound by gravitational attraction. You will discover the appropriate response fascinating.

Answer –                                     

We know that the radius of the first Bohr orbit is given by the relation –

    \[{{r}_{1}}=\frac{4\pi {{\in }_{0}}{{\left( \frac{h}{2\pi } \right)}^{^{2}}}}{{{m}_{e}}{{e}^{2}}}\]

Where,

∈0 is the Permittivity of free space

h is the Planck’s constant = 6.63 × 10−34 J s

me is the Mass of an electron = 9.1 × 10−31 kg

e is the Charge of an electron = 1.9 × 10−19 C

mp is the Mass of a proton = 1.67 × 10−27 kg

r is the Distance between the electron and the proton

we know that the coulomb attraction between an electron and a proton is given by the relation –

    \[{{F}_{c}}=\frac{{{e}^{2}}}{4\pi {{\in }_{0}}{{r}^{2}}}\]

Also the gravitational force of attraction between an electron and a proton is given by –

    \[{{F}_{G}}=\frac{G{{m}_{e}}{{m}_{p}}}{{{r}^{2}}}\]

Where,

G is the Gravitational constant, given = 6.67 × 10−11 N m2/kg2

Considering that the electrostatic and the gravitational force between an electron and a proton are equal, we get the following relation –

∴ FG = FC

Upon substituting values we get

    \[\frac{G{{m}_{e}}{{m}_{p}}}{{{r}^{2}}}=\frac{{{e}^{2}}}{4\pi {{\in }_{0}}{{r}^{2}}}\]

    \[G{{m}_{e}}{{m}_{p}}=\frac{{{e}^{2}}}{4\pi {{\in }_{0}}}\]

Substituting the values from above in the first equation of radius, we get –

    \[{{r}_{1}}=\frac{{{\left( \frac{h}{2\pi } \right)}^{2}}}{G{{m}_{e}}{{m}_{p}}}\]

    \[{{r}_{1}}=\frac{{{\left( \frac{6.64\times {{10}^{-34}}}{2\times 3.14} \right)}^{2}}}{6.67\times {{10}^{-11}}\times 1.67\times {{10}^{-27}}\times {{\left( 9.1\times {{10}^{-31}} \right)}^{2}}}\]

    \[{{r}_{1}}=1.21\times {{10}^{29}}m\]

It is known that the universe is 1.5 × 1027 m wide. Hence, it can be concluded that the radius of the first Bohr orbit is much greater than the estimated size of universe.

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