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If the kinetic energy of the electron in the hydrogen atom is (e²)/(8πε₀r), then its potential energy is ______.

Asked in GUJCET 2019 · Energy levels and ionisation

• (1) (e²)/(4πε₀r)
• (2) -(e²)/(4πε₀r)
• (3) (e²)/(8πε₀r)
• (4) -(e²)/(8πε₀r)

Step-by-step solution

Why the other options are wrong

• (1) The size is right but the sign is not: the electron and proton attract, so their potential energy (zero at infinite separation) is negative.
• (3) This is the given kinetic energy copied across; the potential energy is twice as large in size and negative.
• (4) -(e²)/(8πε₀r) is the total energy, E=K+U=-K, not the potential energy.

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