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In the Bohr model of a hydrogen atom, if the kinetic energy is expressed as k = kZe² / 2rₙ, what is the expression for the total energy?

1. E = -kZe² / 2rₙ
2. The ratio of kinetic energy to total energy is 1 : -1
3. Total energy equals -kZe² / 2rₙ
4. None of these

Correct answer: E = -kZe² / 2rₙ

Solution

In the Bohr model, the total energy of an electron in orbit is equal to the negative of its kinetic energy, i.e., E = -kZe² / 2rₙ. This is because the total energy is the sum of kinetic and potential energy, and the potential energy is twice the magnitude of the kinetic energy but negative.

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