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प्रश्न
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?
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उत्तर
The ratio of the electrostatic force to the gravitational force between an electron and a proton is
`(F_"elec")/(F_"grav") = (K_(e.e)/r^2)/((G m_e m_p)/r^2)`
= `(Ke^2)/(Gm_em_p)`
In terms of dimensions,
`[(Ke^2)/(Gm_em_p)] = [(F_"elec")/(F_"grav")]`
= `(MLT^-2)/(MLT^-2)`
= 1
Thus, the ratio `(Ke^2)/(Gm_em_p)` is dimensionless
`(Ke^2)/(Gm_em_p)`
= `(9 xx 10^9 xx (1.6 xx 10^-19)^2)/(6.67 xx 10^-11 xx 9.1 xx 10^-31 "kg" xx 1.67 xx 10^-27 "kg")`
= 0.23 × 1040
= 2.3 × 1039
That electrostatic forces are a factor of 1039 more than gravitational forces is indicated by this ratio.
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