Atomic physicists ignore the effect of gravity within an atom. To see why, Calculate and compare the gravitational and electrical forces between an electron and a proton separated by 10^-10 m.
To calculate and compare the gravitational and electrical forces between an electron and a proton separated by a distance of 10^-10 m, we need to use the equations for gravitational force and electrical force.
1. Gravitational Force (Fg):
The gravitational force between two objects can be calculated using Newton's law of universal gravitation:
Fg = (G * m1 * m2) / r^2
Where:
Fg is the gravitational force
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the objects (mass of electron ≈ 9.10938356 x 10^-31 kg, mass of proton ≈ 1.6726219 x 10^-27 kg)
r is the distance between the objects (10^-10 m)
2. Electrical Force (Fe):
The electrical force between two charged particles can be calculated using Coulomb's law:
Fe = (k * |q1| * |q2|) / r^2
Where:
Fe is the electrical force
k is the electrostatic constant (8.9875517923 × 10^9 N m^2/C^2)
|q1| and |q2| are the magnitudes of the charges (charge of electron ≈ 1.602176634 x 10^-19 C, charge of proton ≈ 1.602176634 x 10^-19 C)
r is the distance between the charges (10^-10 m)
Now let's calculate the gravitational and electrical forces and compare them:
Gravitational force (Fg):
Fg = (G * m1 * m2) / r^2
= (6.67430 × 10^-11 N m^2/kg^2) * (9.10938356 x 10^-31 kg) * (1.6726219 x 10^-27 kg) / (10^-10 m)^2
Electrical force (Fe):
Fe = (k * |q1| * |q2|) / r^2
= (8.9875517923 × 10^9 N m^2/C^2) * (1.602176634 x 10^-19 C) * (1.602176634 x 10^-19 C) / (10^-10 m)^2
By calculating these two forces, we can compare their magnitudes to see if one significantly dominates over the other. However, it is important to note that in the context of atomic physics, the electrical force is much stronger than the gravitational force by many orders of magnitude. Because the electrical forces are so much stronger, physicists usually ignore the effect of gravity within an atom.
Let us know what you find out. Use Newton's and Coulomb's laws. The ratio is about 10^39, as I recall. The electrostatic force is the higher one.
You will need to use the electron charge and the electron and proton mass.