Question

Compare the gravitational and electrical forces between an electron and a proton in the hydrogen atom (separated by 10^-10 m). What is the order of magnitude of the ratio of the electrical to gravitational force?

Answer 1

The ratio of the electrical to gravitational force between the electron and a proton in Hydrogen atom is 0.227 x 10⁴⁰.

What is electrostatic force?

The electrostatic force F between two charged objects placed distance apart is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.

F = kq₁q₂/d²

where k = 9 x 10⁹ N.m²/C²

The magnitude of charge on electron is equal to charge on proton =e = 1.6 x 10⁻¹⁹ C.

Fe =  9 x 10⁹ x ( 1.6 x 10⁻¹⁹)² /(10⁻¹⁰)²

Fe = 23.04 x 10⁻⁹ N

The gravitational force of attraction law states that the force of attraction is directly proportional to the product of masses of the object and inversely proportional to the square of distance between them.

F = Gm₁ m₂ / d²

where , Gravitational constant G = 6.67 x 10⁻¹¹ N.m²/kg²

Mass of electron, me = 9.11 x 10⁻³¹ kg and mass of proton in hydrogen atom mp = 1.67 x 10⁻²⁷ kg.

Substituting the values, we get the gravitational force,

Fg= 6.67 x 10⁻¹¹x 9.11 x 10⁻³¹ x  1.67 x 10⁻²⁷ /(10⁻¹⁰)²

Fg = 101.475 x 10⁻⁴⁹ N

The ratio of the electrical to gravitational force is

Fe/Fg = 23.04 x 10⁻⁹ N / 101.475 x 10⁻⁴⁹ N

Fe/Fg = 0.227 x 10⁴⁰

Thus, the ratio of the electrical to gravitational force is 0.227 x 10⁴⁰ .

Learn more about electrostatic force.

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