In the Bohr’s model of hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in nth quantum state is

Options

(a) (-1)
(b) (+1)
(c) (-2)
(d) (+2)

Correct Answer:

(-1)

Explanation:

In Bohr’s model of hydrogen atom, the kinetic energy of the electron in nᵗʰ state is given by
K = me⁴ / 8ε₀²h²n² = (13.6 / n²) eV
where, me⁴ / 8ε₀²h² = 13.6 eV
The potential energy of electron in nᵗʰ state is given by
U = -2me⁴ / 8ε₀²h²n² = (-27.2 / n²) eV
Total energy of electron in nᵗʰ state is given by
E = K + U = (me⁴ / 8ε₀²h²n² ) – (2me⁴ / 8ε₀²h²n²)
E = -me⁴ / 8ε₀²h²n² = (-13.6 / n ²) eV
.·. K / E = -1