Question
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?
Solution
The given ratio is
`(ke^2)/(Gm_cm_p)`
Where,
G = Gravitational constant
Its unit is N m2 kg−2.
me and mp = Masses of electron and proton.
Their unit is kg.
e = Electric charge.
Its unit is C.
k=A constant
`=1/(4piin_0)`
∈0 = Permittivity of free space
Its unit is N m2 C−2.
therefore, unit of the given ratio `(ke^2)/(Gm_cm_p)=([Nm^2C^-2][c^-2])/([Nm^2kg^-2][kg][kg])=m^0L^0T^0`
Hence, the given ratio is dimensionless.
e = 1.6 × 10−19 C
G = 6.67 × 10−11 N m2 kg-2
me= 9.1 × 10−31 kg
mp = 1.66 × 10−27 kg
Hence, the numerical value of the given ratio is
`(ke^2)/(Gm_cm_p)=(9xx10^9xx(1.6xx10^-19)^2)/(6.67xx10^-1xx9.1xx10^-3xx1.67xx10^-22)~~2.3xx10^39`
This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.
