There are extremely large electrical forces of repul- sion between the protons i

Question

There are extremely large electrical forces of repul- sion between the protons in the nucleus of an atom However, these forces are normally not as great as the "strong force," which is the force that binds all the protons and neutrons in the nucleus together, The strong force has a very short range-on the order of 2 X 10-15 m, When protons or neutrons are separated by a distance greater than this, the strong force does not act. Thus, if for some reason a nucleus splits in two, or "fissions," each fragment can experience an electrical repulsive force without any other force to balance it. Suppose a uranium nucleus (92 protons) splits into two nuclei having 46 protons each 65

Explanation / Answer

Gravitational force = G x m1 x m2 /d2

where G= gravitational constant = 6.674 x 10-11 N. m2 /kg2

m1= mass of a proton = 1.672 x 10-27 kg

m2= mass of electron =9.1 x 10-31 kg

so gravitational force at an arbitrary distance d=  6.674 x 10-11 x 1.672 x 10-27 x 9.1 x 10-31/d2

=1.01 x 10-67 /d2 N

Electrical force = kq1q2/d2

where k = 9 x 109

q1= charge of proton = 1.6 x 10-19 c

q2= charge of electron = 1.6 x 10-19 c

so electrical force at an arbitrary distance d= 9 x 109 x 1.6 x 10-19 x 1.6 x 10-19/d2

=2.3 x 10-28 /d2 N

So ratio of magnitudes of the electrical and gravitational force between a proton and an electron = (2.3 x 10-28 /d2)/(1.01 x 10-67 /d2) =2.277 x 1039

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