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If the potential energy of the electron in the hydrogen atom is -(e²)/(4πε₀ r), then what is its kinetic energy?

Asked in GSEB Board March 2019 · Energy levels and ionisation

• (1) (e²)/(8πε₀ r)
• (2) -(e²)/(4πε₀ r)
• (3) -(e²)/(8πε₀ r)
• (4) (e²)/(4πε₀ r)

Step-by-step solution

Why the other options are wrong

• (2) comes from this repeats the potential energy itself; a kinetic energy cannot be negative.
• (3) -(e²)/(8πε₀ r) is the total energy, E=K+U=U/2; the kinetic energy has the same size but is positive.
• (4) (e²)/(4πε₀ r) drops the factor 1/2: it makes the kinetic energy as large as the potential energy instead of half as large.

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