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## Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron, FE/FG. Note: k = 8.99 × 109 N-m2

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## Answers ( )

Answer:Explanation:The gravitational force is given by Newton’s Law of Gravity:

The electrostatic force is given by Coulomb’s Law:

The ratio between these two forces is

Complete Question:Determine the ratio of the electrostatic force to the gravitational force between a proton and electron, FE/FG.

Note : k = 8.99 × 10⁹ N.m²/C² ; G = 6.672 x 10⁻¹¹ Nm²/kg²; me = 9.109 × 10⁻³¹ kg and mp = 1.672 × 10⁻²⁷kg.

Answer:FE/FG = 2.3 x 10³⁹

Explanation:According to Coulomb’s law, the electrostatic force () between two particles is given as;

= k x ——————–(i)

Where;

k = electric constant = 8.99 x 10⁹Nm²/C²

Q₁ = the charge of particle 1

Q₂ = the charge of particle 2

r = the distance of separation between the two particles

Also, according to Newton’s law of gravitational force, the gravitational force () between two particles is given as;

= G x ——————–(ii)

Where;

G = gravitational constant = 6.672 x 10⁻¹¹Nm²/kg²

M₁ = mass of particle 1

M₂ = mass of particle 2

r = distance of separation between the two particles

For clarity, we will calculate and separately before finding their ratio.

From the question;

The particles are a proton (particle 1) and an electron (particle 2) with the following details;

Q₁ = charge of proton = 1.6 x 10⁻¹⁹C

Q₂ = charge of electron = -1.6 x 10⁻¹⁹C

M₁ = mass of proton = mp = 1.672 × 10⁻²⁷kg

M₂ = mass of electron = me = 9.109 × 10⁻³¹kg

Substitute the values of k, Q₁ and Q₂ into equation (i) as follows;

= 8.99 x 10⁹ x

= 8.99 x 10⁹ x [negative sign can be discarded]

=

Also, substitute the values of G, M₁ and M₂ into equation (ii) as follows;

= 6.67 x 10⁻¹¹ x

= 6.67 x 10⁻¹¹ x

=

The ratio / is therefore;

/ = /

/ =

/ =

/ =

Therefore, the ratio is 2.3 x 10³⁹