Compute the gravitational force and the electric force between the electron and the proton in the hydrogen atom if they are 5.3 x 10-11 meters apart. Then calculate the ratio of Fe to Fg.

Fg = 3.61×10⁻⁴⁷ N.

Fe = 8.2× 10⁻⁸ N.

Fe/Fg = 2.27×10³⁹

Explanation:

From Newton's law of gravitational force ofattraction,

Gravitational force of attraction, Fg = Gm1m2/r²

Where,

m1 = mass of electron

= 9.1 x 10⁻³¹ kg

m2 = mass of protron

= 1.67 x 10⁻²⁷ kg

r = distance between proton and electron

= 5.3×10⁻¹¹ m

G = Gravitational constant

= 6.67×10⁻¹¹ Nm²/kg²

Therefore,

Fg = (1.67 x 10⁻²⁷ × 9.1×10⁻³¹ × 6.67×10⁻¹¹)/( 5.3×10⁻¹¹)²

= 3.6085 × 10⁻⁴⁷ N.

From coulomb's law,

Electric force, Fe = kq1q2/r²

Where,

q1 = charge of proton

= 1.6×10⁻¹⁹ C

q2 = charge of electron

= 1.6×10⁻¹⁹ C

r = distance between proton and electron.

= 5.3×10⁻¹¹ m

k = 9.0×10⁹ Nm²/C²

Fe = (1.6×10⁻¹⁹ × 1.6×10⁻¹⁹ × 9.0×10⁹)/(5.3×10⁻¹¹)²

= 8.202 × 10⁻⁸ N.

Therefore, ratio of Fe to Fg:

Fe/Fg = 8.202 × 10⁻⁸/3.6085 × 10⁻⁴⁷

= 2.273 × 10³⁹

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