Atomic physicits 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 to the -10 m.--
To compare the gravitational and electrical forces between an electron and a proton separated by a distance of 10^-10 meters, we can use the equations for these forces.
First, let's start with the gravitational force. The formula to calculate the gravitational force between two objects is given by Newton's Law of Universal Gravitation:
F_grav = (G * m1 * m2) / r^2
Where:
F_grav = gravitational force
G = gravitational constant (approximately 6.67430 × 10^-11 N*m^2/kg^2)
m1, m2 = masses of the two objects
r = distance between the two objects
Now, let's consider the electrical force between the electron and proton. The electrical force is given by Coulomb's Law:
F_elec = (k * |q1 * q2|) / r^2
Where:
F_elec = electrical force
k = Coulomb's constant (approximately 8.98755 × 10^9 N*m^2/C^2)
q1, q2 = charges of the two objects
r = distance between the two objects
In this case, the electron has a charge of -1.6 × 10^-19 C (coulombs), and the proton has a charge of +1.6 × 10^-19 C.
Now, let's calculate the gravitational and electrical forces:
Gravitational Force:
F_grav = (6.67430 × 10^-11 N*m^2/kg^2) * (9.1 × 10^-31 kg) * (1.67 × 10^-27 kg) / (10^-10 m)^2
Electrical Force:
F_elec = (8.98755 × 10^9 N*m^2/C^2) * (| -1.6 × 10^-19 C * 1.6 × 10^-19 C |) / (10^-10 m)^2
After plugging in the values and performing the calculations, we find that:
Gravitational Force ≈ 6.73 × 10^-47 N
Electrical Force ≈ 2.3 × 10^-8 N
Comparing these two forces, we can see that the electrical force is much stronger than the gravitational force, by a factor of approximately 10^39.
Therefore, atomic physicists ignore the effect of gravity within an atom because the gravitational force between the electron and proton is negligibly small compared to the electrical force. Gravity plays a significant role only in objects with much larger masses, such as planets or stars.