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Question

According to Rutherford's model, what will be the kinetic energy of an electron of mass me at a distance r from the center of a Li++ ion? (The Lithium nucleus has three protons.)

A
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B
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C
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D
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Solution

The correct option is A
The atomic number of Lithium is Z=3, which means it has three protons in the nucleus, having a total positive charge of (+Ze). An electron's charge is (−e). Since the centripetal acceleration is provided by the electrostatic force, we can write -
mev2r=Ze24πϵ0r2
mev2=Ze24πϵ0r
12mev2= kinetic energy of the electron = Ze28πϵ0r=3e28πϵ0r.

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