Question

An alpha particle consists of two protons and two neutrons with a mass of 6.64 x 1027 kg and charge 3.2 x 10-19 C. If two of them are separated by a distance R, using Coulomb's Law and the Universal Law of Gravitation, calculate the ratio of the electric force to the gravitational force acting on each. Do you think this is a surprising number?

Answer 1

Answer:  ratio = 3.14 × 10³⁵

Explanation:

From Newtons law of Universal Gravitation;

Every object in the universe is attracted to every other object

F = (Gm₁m₂)/r²

G = 6.67 X 10⁻¹¹ N-m²/kg²

M₁= mass of one object

M₂= mass of second object

r = distance from center of objects

q = charge = 3.2 x 10⁻¹⁹C.

• Calculating the gravitational force;

Fg = (Gm₁m₂)/r² = (Gm²)/r²

which is = (6.67×10⁻¹¹ × (6.64×10⁻²⁷)²) / r²

= (2.94 × 10⁻⁶³) / r²

• Calculating the electric force;

Fe = (Kq₁q₂) / r² = K q² / r² = (9×10⁹ × (3.2 × 10⁻¹⁹)² / r²

Fe = 9.22 × 10⁻²⁸ / r²

comparing the ratio of both forces we have;

Fe/Fg = (9.22×10⁻²⁸/r²) ÷ (2.94×10⁻⁶³/r²)

r² cancels from the above expression, which gives;

ratio as 3.14 × 10³⁵