What is the ratio of the magnitude of the electric force between the 3rd electron and 3rd proton in a lithium atom to the magnitude of the gravitational attraction between them?
-
The electric force Fe = kq₁q₂/d² (Coulomb's Law)
The gravitational force Fg =Gm₁m₂/d² (Coulomb's Law)
Ratio = Fe/Fe = (kq₁q₂/d²) / (Gm₁m₂/d²)
= (kq₁q₂)/(Gm₁m₂) (note the distance squared has cancelled - so the ratio is the same at any distance)
You just need to do the arithmetic for yourself - plug in these values:
k = Coulomb 's constant = 9x10⁹ Nm²/C²
q₁ = q₂ = 1.6x10⁻¹⁹C (ignore sign as you are comparing magnitudes)
m₁ = 9.11x10⁻³¹ kg (mass of electron)
m₂ = 1.67 x 10⁻²⁷ kg (mass of proton)
G = 6.67 × 10⁻¹¹ Nm²/kg² (universal constant of gravitation)
The answer should turn out very large, as gravity is incredibly weak.
The fact that is the '3rd electron' and '3rd proton' in lithium makes no difference at all - that's just to test your understanding to check if you can see through the irrelevant detail to the underlying physics.
The gravitational force Fg =Gm₁m₂/d² (Coulomb's Law)
Ratio = Fe/Fe = (kq₁q₂/d²) / (Gm₁m₂/d²)
= (kq₁q₂)/(Gm₁m₂) (note the distance squared has cancelled - so the ratio is the same at any distance)
You just need to do the arithmetic for yourself - plug in these values:
k = Coulomb 's constant = 9x10⁹ Nm²/C²
q₁ = q₂ = 1.6x10⁻¹⁹C (ignore sign as you are comparing magnitudes)
m₁ = 9.11x10⁻³¹ kg (mass of electron)
m₂ = 1.67 x 10⁻²⁷ kg (mass of proton)
G = 6.67 × 10⁻¹¹ Nm²/kg² (universal constant of gravitation)
The answer should turn out very large, as gravity is incredibly weak.
The fact that is the '3rd electron' and '3rd proton' in lithium makes no difference at all - that's just to test your understanding to check if you can see through the irrelevant detail to the underlying physics.
-
kq^2/G*me*mp where q is the charge on electron/proton, me is the electron mass, mp is proton mass, k=9e9 and G is the gravitational constant 6.67e-11
The distance between them squared cancels since it is in both denominators
The distance between them squared cancels since it is in both denominators