Question

(a) two protons in a molecule are 4.50 10-10m apart. find the magnitude of the electric force exerted by one proton on the other.

(b) State how the magnitude of this force compares with the magnitude of the gravitational force exerted by one proton on the other.
(c) What If? What must be a particle's charge-to-mass ratio if the magnitude of the gravitation force between two of these particles is equal to the magnitude of electrical force between them?

Answer 1

a) 1. 1365 × 10⁻⁹N

b) 9.1862 × 10⁻⁴⁶N

c) 8.61 × 10⁻¹¹C/Kg

Step-by-step explanation:

Ke = 8.99× 109 N.m2 / C2 , G = 6.67 × 10-11 N. m2 / kg2

a) F = Ke . q₁.q₂/r²

= (8.99× 109 N.m2 / C2 ) ×(1.60×10⁻¹⁹C)²/(4.50×10⁻¹⁰C)²

= 1. 1365 × 10⁻⁹N

b)

F = Gm₁m₂/r²

= (6.67× 10⁻¹¹)×(1.67×10⁻²⁷)²/(4.50×10⁻¹⁰)²

= 9.1862 × 10⁻⁴⁶N

The electric force is larger by 8.0497 ×10³⁷ times

c)

if Keq₁q₂/r² Gm₁m₂/r²,

with q₁=q₂ = q, and m₁ =m₂ = m

Then q/m =
`√(G/M)` =
`\sqrt{(6.67 X 10^(-11) } /8.89 X 10^(9)`

= 8.61 × 10⁻¹¹C/Kg