In the usual convention, the energy of a free electron infinitely far from a hydrogen nucleus is taken as zero. Suppose instead that the energy of the electron in the fifth Bohr orbit is defined to be zero. What is the energy assigned to the hydrogen ground state on this new scale?
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Question

In the usual convention, the energy of a free electron infinitely far from a hydrogen nucleus is taken as zero. Suppose instead that the energy of the electron in the fifth Bohr orbit is defined to be zero. What is the energy assigned to the hydrogen ground state on this new scale?

Options

G1 Physics · Accepted Answer

On the usual scale: E₁ = −13.6 eV. For the fifth orbit: E₅ = −13.6 ÷ 25 = −0.544 eV. To make the fifth-orbit energy zero, subtract E₅ from every old energy: E′ = E−E₅. Therefore, E′₁ = −13.6−(−0.544) = −13.056 eV. Correct option: B.