Sure, I can help you with that.
The ratio ke^2 / G memp is dimensionless, which means that it has no units. This is because the units of ke^2 are Nm^2 C^-2, the units of G are Nm^2 kg^-2, the units of me are kg, and the units of mp are kg. When we divide these units, all of the units cancel out, leaving us with a dimensionless quantity.
The value of the ratio ke^2 / G memp is approximately 2.29 × 10^39. This means that the electrostatic force between an electron and a proton is 2.29 × 10^39 times stronger than the gravitational force between an electron and a proton.
The ratio ke^2 / G memp signifies the relative strength of the electrostatic force and the gravitational force. The fact that the ratio is so large means that the electrostatic force is much stronger than the gravitational force. This is why electrons and protons are bound together in atoms, even though the gravitational force between them is very weak.
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Coulomb's constant | k | 8.987551787 × 10^9 | Nm^2 C^-2 |
| Gravitational constant | G | 6.67408 × 10^−11 | Nm^2 kg^-2 |
| Mass of electron | me | 9.1093837 × 10^−31 | kg |
| Mass of proton | mp | 1.672621777 × 10^−27 | kg |
I hope this helps! Let me know if you have any other questions.