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If the potential energy of electron in the hydrogen atom is -(ke²)/r, then what is its kinetic energy?

Asked in GSEB Board July 2015 · Energy levels and ionisation

Answer: (2) (ke²)/(2r)

Step-by-step solution

Given: potential energy U=-(ke²)/r, where k=1/(4πε₀).

Idea: the Coulomb attraction of the proton supplies the centripetal force on the orbiting electron.

(mv²)/r=(ke²)/(r²), so mv²=(ke²)/r.

K=1/2mv²=(ke²)/(2r).

So the kinetic energy is positive and half the size of the potential energy: K=-U/2=(ke²)/(2r).

Why the other options are wrong

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