Question

How far away can a proton and an electron be from each other, such that they still exert an electric force on each other of magnitude F? (Your answer should show why gravity is unimportant on the molecular scale!)

Answer 1

Answer:

$\sqrt{ \frac{2.3 *10^{-28} }{F} }$

Explanation:

Total force = Force due to gravity + Force due to charges

Total force = $\frac{GMm}{r^{2} } + \frac{kQq}{r^{2} }$

r is the separation between particles.

Charge of a proton(Q) = - (charge of an electron(q) ) = 1.6 * 10^-19 coulombs

Mass of a proton (M)= 1.67×10^-27 kilograms

Mass of an electron (m) =9.11 × 10^-31 kilograms

G=6.67 ×10^−11 N⋅m^2/kg^2

k=8.99 * 10 ^9 N.m^2 / C^2

Plugging in values:

Force due to gravity= (6.67 *10^−11)(1.67 * 10^-27)*(9.11 * 10^-31) /r^2 =1.01 * 10^-67   /  r^2

Force due to charges : (8.99 * 10 ^9)*(1.6 * 10^-19)*(1.6 * 10^-19) / r^2 = 2.3 *10^-28    /  r^2

We can observe that force due to charges is too large as compared with force due to charge. The ratio of Fc to Fm is 2.3* 10^39. It means that we can ignore force due to gravity.

Total force = Force due to charges.

F = 2.3 *10^-28    /  r^2

r = $\sqrt{ \frac{2.3 *10^{-28} }{F} }$