The nucleus of the helium atom contains two protons that are separated by about 3.0 x 10-15 m. Find the magnitude of the electrostatic force that each proton exerts on the other
Coulombs law applies.
To find the magnitude of the electrostatic force between two protons in the helium atom, you can use Coulomb's Law. Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for the magnitude of the electrostatic force (F) between two charges is:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2)
- q1 and q2 are the charges of the two particles
- r is the distance between the two particles
In this case, the charges on the two protons are the same (both are positive), so we can multiply the charges together to get the product of their charges.
Let's calculate the force:
F = (8.99 x 10^9 N m^2/C^2 * |2e * 2e|) / (3.0 x 10^-15 m)^2
1. Convert the elementary charge (e) to Coulombs:
- 1 elementary charge (e) = 1.60 x 10^-19 C
- Therefore, 2e = 2 * 1.60 x 10^-19 C = 3.20 x 10^-19 C
2. Plug in the known values into the formula:
F = (8.99 x 10^9 N m^2/C^2 * |3.20 x 10^-19 C * 3.20 x 10^-19 C|) / (3.0 x 10^-15 m)^2
3. Calculate the magnitude of the force:
F = (8.99 x 10^9 N m^2/C^2 * 10.24 x 10^-38 C^2) / 9.0 x 10^-30 m^2
= 89.9 x 10^-9 N
Therefore, the magnitude of the electrostatic force that each proton exerts on the other in the helium atom is approximately 89.9 x 10^-9 N.