Solution

In the Bohr–Sommerfeld model, an electron in an elliptical orbit around a nucleus obeys a modified form of Kepler's third law. For a hydrogen-like atom, the square of the orbital period $T$ is proportional to the cube of the semi-major axis $a$. Consider an electron in an elliptical orbit with a semi-major axis $a = 2.12 \times 10^{-10}\,\text{m}$ (four times the Bohr radius) and an eccentricity $e = 0.30$. The constant of proportionality for hydrogen is $k = 2.96 \times 10^{-16}\,\text{s}^2/\text{m}^3$.