The mass of an electron is 9.109 x 10⁻³¹ kg
The weight of the electron is (mass) x (g) = 8.926 x 10⁻³⁰ Newton
The charge on an electron is -1.602 x 10⁻¹⁹ Coulomb
The repelling force between the two electrons is (K · q₁ · q₂ / r²) =
(8.98755 x 10⁹ N-m²/C²) x (1.602 x 10⁻¹⁹ C)² / D²
In order for the bottom one to just exactly hold the top one up at a distance 'D', the repelling force has to be exactly equal to the weight of the upper electron.
8.926 x 10⁻³⁰ N = (8.98755 x 10⁹ N-m²/C²)·(1.602 x 10⁻¹⁹ C)² / D²
We have to solve THAT ugly mess for ' D '.
Clean up the units first:
Cancel the C² on the right side, then divide each side by Newton:
8.926 x 10⁻³⁰ = (8.98755 x 10⁹ m²) x (1.602 x 10⁻¹⁹)² / D²
Now, let's multiply both sides by (D² x 10²⁹) :
D² x 8.926 x 10⁻¹ = (8.98755 m²) x (1.602)²
Divide each side by (0.8926):
D² = (8.98755 x 1.602²) / (0.8926) meter²
D² = 25.84 m²
Take the square root of each side:
<em>D = 5.08 meters</em>
I am shocked, impressed, and amazed !
Are you shocked, impressed, or amazed ?
