Answer:
Fg = 3.61×10⁻⁴⁷ N.
Fe = 8.2× 10⁻⁸ N.
Fe/Fg = 2.27×10³⁹
Explanation:
From Newton' s law,
Fg = Gm'm/r²...................... Equation 1
Where Fg = gravitational force, m = mass of proton, m' = mass of electron, r = distance between proton and electron, G = Gravitational constant
Given: m = 1.67 x 10⁻²⁷ kg, m' = 9.1×10⁻³¹ kg, r = 5.3×10⁻¹¹ m
Constant: G = 6.67×10⁻¹¹ Nm²/kg²
Substitute into equation 1
Fg = (1.67 x 10⁻²⁷)( 9.1×10⁻³¹ )(6.67×10⁻¹¹)/( 5.3×10⁻¹¹)²
Fg = (101.364×10⁻⁶⁹)/(28.09×10⁻²²)
Fg = 3.61×10⁻⁴⁷ N.
From coulomb's law,
Fe = kqq'/r²................. Equation 2
Where Fe = Electric force, q = charge of proton, q' = charge of electron, r = distance between proton and electron.
Given: q = 1.6×10⁻¹⁹ C, q' = 1.6×10⁻¹⁹ C, r = 5.3×10⁻¹¹ m, k = 9.0×10⁹ Nm²/C².
Substitute into equation 2
Fe = (1.6×10⁻¹⁹)(1.6×10⁻¹⁹)(9.0×10⁹)/(5.3×10⁻¹¹)²
Fe = 23.04×10⁻²⁹/(28.09×10⁻²²)
Fe = 8.2× 10⁻⁸ N.
Therefore,
Fe/Fg = 8.2× 10⁻⁸ /3.61×10⁻⁴⁷
Fe/Fg = 2.27×10³⁹
