Check that the ratio ke2/G memp is dimensionless. Look up a Table of physical constants and determine the value of this ratio

Check that the ratio ke²/G m_em_p is dimensionless. Look up a Table of physical constants and determine the value of this ratio. What does the ratio signify?

Solution:

Use the table of physical constants we get

Unit of

G  = N m²kg⁻².

m_e = Kg

m_p = Kg       (Masses of electron and proton)

e = C           (e is electric charge)

k = 1/4πε0  = Nm²C^-2

Plug the values of the units, we get

= N⁰m⁰C⁰Kg⁰

 ( given : Check that the ratio ke²/G m_em_p is dimensionless )

All units have canceled out hence it is a ratio, because ratio has no unit  

Hence

Values of all variable or constant 

Charge in electron , e = 6 × 10⁻¹⁹ C

Gravitational constant G = 6.67 × 10⁻¹¹ N m² kg^-2

Mass of electron, m_e= 9.1 × 10⁻³¹ kg

Mass of proton , m_p= 1.66 × 10⁻²⁷ kg

Plug the values 

Ratio is nearly equal to 2.3 × 10 ³⁹.