Question

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of a hydrogen atom is

• A. \(1: -1\)
• B. \(1: 3\)
• C. \(-1: 2\)
• D. \(2: -5\)

Hint:

In the Bohr model of the hydrogen atom, the total energy is negative, indicating a bound state, and the kinetic energy is half the magnitude of the potential energy.

Answer 1

The Correct Option is A

In a Bohr orbit, the total energy \( E \) of an electron is the sum of its kinetic energy \( K \) and potential energy \( U \): \[ E = K + U \] For a hydrogen atom, the potential energy \( U \) is given by: \[ U = -2K \] Thus, the total energy \( E \) is: \[ E = K - 2K = -K \] The ratio of kinetic energy to total energy is: \[ \frac{K}{E} = \frac{K}{-K} = -1 \] Therefore, the ratio is \(1: -1\).