Question

Compare the electrostatic force between an electron and proton separated by 0.530×10−10 m with the gravitational force between them. This distance is their average separation in a hydrogen atom. me = 9.11×10–31 kg mp = 1.67×10–27 kg

Answer 1

The electrostatic force between an electron and proton is much stronger than the gravitational force.

Step-by-step explanation:

The electrostatic force between an electron and proton can be calculated using Coulomb's Law. The formula is given as: F = k × (q1 × q2) / r^2

Where F is the electrostatic force, k is the Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the particles (in this case -1.6 x 10^-19 C for electron and +1.6 x 10^-19 C for proton), and r is the separation distance between the particles (0.53 x 10^-10 m).

The gravitational force between the electron and proton can be calculated using Newton's Law of Universal Gravitation: F = G × (m1 × m2) / r^2

Where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the particles (9.11 x 10^-31 kg for electron and 1.67 x 10^-27 kg for proton), and r is the separation distance between the particles (0.53 x 10^-10 m).

By plugging in the values into both equations, we can find the magnitudes of both forces. Comparing the values, we see that the electrostatic force between the electron and proton is much stronger than the gravitational force.

Answer 2

Answer: The electrostatic force is 2.62 x 10^45 times greater than the gravitational force

Step-by-step explanation:

According to columb's law, the electrostatic force F is given mathematical as

F =K* q1 *q2/ r²

K= electrostatic constant = 9 x 10^9 Nm²/c^-2

q1 = 1.609 x 10^-16c

q2 = 1.609 x 10^-16c

r = 0.530 x 10^-10m

F= 9x10^9 * 1.609x10^-16 * 1.609x 10^-16/ (0.530 x 10^-10)²

F = 23.299 x 10^-23/ 0.289 x 10^-20

F = 8.29 x 10^-2 N

To get the gravitational force F', we use newton' law of gravitation which is given below as

F' = G *Me * Mp / r²

Where G= gravitational constant = 6.674 x 10^-11

Me = mass of electron = 9.11×10^–31 kg

Mp = mass of proton = 1.67×10^-27 kg

r = distance between proton and electron =0.530 x 10^-10m

F' = (6.674 x 10^-11) * (9.11×10^–31) * (1.67×10^-27)/ (0.530 x 10^-10)²

F' = 101.53 x 10^-69/ 0.2809 x 10^-20

F' = 3.164 x 10^-47 N

It is obvious that electrostatic force is greater than that of gravitational, to know how much, we divide electrostatic force by gravitational.

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F/F' = 8.294 x 10^-2/ 3.164 x 10^-47 = 2.62 x 10^45

Thus the electrostatic force is 2.62 x 10^45 times greater than the gravitational.