One of the earliest problems with the Rutherford model of the atom was the fact

Question

One of the earliest problems with the Rutherford model of the atom was the fact that the protons are confined in an extremely small space called the nucleus. The two protons in a helium nucleus clearly repel each other strongly and should move rapidly apart. Assume for this problem that the strong force does not exist and that protons are point particles (they are not). If two protons start with a separation of 1.00 * 10-15 m, calculate the velocity that they will have when they are very far apart.

Explanation / Answer

r = initial separation = 1 x 10-15 m

V = velocity far apart

using conservation of energy

Electric Potential energy = Kinetic energy

k q2/r = (0.5) m V2 + (0.5) m V2

(9 x 109) (1.6 x 10-19)/(1 x 10-15) = (1.67 x 10-27) V2

V = 1.2 x 107 m/s

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