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

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.