Check that the ratio {ke2} /{G me mp} is dimensionless.
Answers
We know very well
k = 9 × 109 Nm2 C‒2
e = 1.6 × 10‒19 C
G = 6.6 × 10‒11 Nm2 kg‒2
me = 9.11 × 10‒31 kg
mp = 1.6 × 10‒27 kg
Putting these values in{ke2} /{G me mp} its value is 2.29 × 1039.
Ratio = {ke2} /{G me mp} = {[Nm2 C‒2] [C]}/{[Nm2 kg‒2] [kg] [kg]} = 1
Hence, the given ration is dimensionless.
The ratio signifies that electrical forces are immensely stronger than the gravitational forces.
Answer:
Use the table of physical constants we get
Unit of
G = N m2 kg−2.
me = Kg
mp = 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
Coulomb’s law
=> F = 1/(4πe0) |q1 q2|/r²
=> N0m0C0Kg0
( given : Check that the ratio ke2/G memp 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, me= 9.1 × 10^−31 kg
Mass of proton , mp = 1.66 × 10^−27 kg
Putting the values
ke²/GMeMp = 9*10^9 * (1.6*10^-19)²/6.67 × 10^−11* 9.1 × 10^−31*1.66 × 10^−27
Ratio is nearly equal to 2.3 × 10 39.