Check that the ratio ke²/G m_em_pis dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

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Solution

The given ratio is .

Where,

G = Gravitational constant

Its unit is N m²kg⁻².

m_e and m_p = Masses of electron and proton.

Their unit is kg.

e = Electric charge.

Its unit is C.

∈₀ = Permittivity of free space

Its unit is N m²C⁻².

Hence, the given ratio is dimensionless.

e = 1.6 × 10⁻¹⁹C

G = 6.67 × 10⁻¹¹ N m²kg^-2

m_e= 9.1 × 10⁻³¹kg

m_p = 1.66 × 10⁻²⁷kg

Hence, the numerical value of the given ratio is

This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.

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Check that the ratio ke2/G memp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Check that the ratio ke²/G m_em_pis dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?