Check that the ratio `ke^(2)//Gm_(e) m_(p)` is dimensionless, Look up a table of Physical Constants and determine the value of this ratio. What does the ratio signify ?

Explanation

To solve the problem step by step, we will check if the ratio \( \frac{ke^2}{G m_e m_p} \) is dimensionless, calculate its value using physical constants, and discuss what the ratio signifies.

### Step 1: Identify the constants and their dimensions

1. **Coulomb's constant \( k \)**:
- Value: \( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)
- Dimensions: \( [k] = \text{M}^1 \text{L}^3 \text{T}^{-2} \text{Q}^{-2} \)

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