Question

An electron at Earth's surface experiences a gravitational force of magnitude F=(9.11×10−31 kg)⋅(9.8 m/s2). Part A How far away can a proton and an electron be from each other, such that they still exert an electric force on each other of magnitude F? (Your answer should show why gravity is unimportant on the molecular scale!)

Answer 1

Answer:

r = 5,085 m

Explanation:

The force exerted by on the surface of the Earth on an electron is its weight

          W = F = 9.11 10⁻³¹  9.8

          W = 8.9 10⁻³⁰ N

The electric force between an electron and a proton is given by Coulomb's Law

         Fe = k q₁ q₂ / r²

         Fe = - k q² / r²

They ask us that W = Fe

         W = k q² / r²

          r = √ k q² / W

Let's calculate

        r = √ 8.99 10⁹ (1.6 10⁻¹⁹)² /8.9 10⁻³⁰

        r = √ 25.86

        r = 5,085 m

Let's look for the relationship of this distance with the harmonic distance

        R / R_atomic = 5,085 / 10⁻¹⁰

        R / R_Atomic = 5 10¹⁰

We see that this distance is 10¹⁰ times the interatomic distance, so the gravitational attraction force is very small at atomic scale

Answer 2

The distance between the proton and electron would be 5.085 m.

This distance is 10¹⁰ times the interatomic distance, therefore, the gravitational force of attraction is very small at atomic scale.

Gravitational force and electrical force

• The gravitational force exerted by earth on a body on the surface of the earth is its weight.

Therefore, the weight of an electron, W = F = 9.11 10⁻³¹ * 9.8

W = 8.93 * 10⁻³⁰ N

• The electrical force between an electron and a proton is given by Coulomb's Law which is given as: Fe = k*q₁q₂ / r²

For the proton and electron;

• Fe = k * q² / r²

where q₁ and q₂ is the charges and r is the distance between the charges;

K is a constant = 8.99 * 10⁹ N⋅m² /C²

q = 1.6 × 10⁻¹⁹ C.

Electrons and protons have equal both opposite charges.

This force Fe would be equal to W, thus:

W = k q² / r²

making r subject of the formula

r = √ k q² / W

r = √ 8.99 *10⁹ (1.6 * 10⁻¹⁹)² /8.9 *10⁻³⁰

r = 5.085 m

Therefore, the distance between the proton and electron would be 5.085 m.

• Comparing this this distance and atomic radii distance

Radius of atom, Ra = 10⁻¹⁰ m

R / Ra = 5.085 / 10⁻¹⁰

R / Ra = 5 *  10¹⁰

From the ratio obtained, this distance is 10¹⁰ times the interatomic distance, therefore, the gravitational force of attraction is very small at atomic scale.

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