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?
The given ratio is Gmcmpke2 Where, G= Gravitational constant Its unit is Nm2kg−2. me and mp= Masses of electron and proton. Their unit is kg. e= Electric charge. Its unit is C. k=A constant =4π∈01 ∈0= Permittivity of free space Its unit is Nm2C−2. Unit of the given ratio Gmcmpke2=[Nm2kg−2][kg][kg][Nm2C2][C−2] =M0L0T0 Hence, the given ratio is dimensionless. e=1.6×10−19C G=6.67×10−11Nm2kg−2 2 me=9.1×106−31kg mp=1.66×10−27kg Gmcmpke2=6.67×10−11×9.1×10−3×1.67×10−229×109×(1.6×10−19)2≈2.3×1039 This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.
