Check that the ratio ke² /Gme mp is dimensionless. Determine the value of this ratio. What does the ratio signify?

Step 1: Check that the ratio $\frac{ke^2}{Gm_e m_p}$ is dimensionless.

First, determine the dimensions of each constant and quantity:

• Dimensions of Coulomb's constant $k$: From Coulomb's Law, $F = k \frac{q_1 q_2}{r^2}$, so $k = \frac{F r^2}{q_1 q_2}$. $$$$