According to de Broglie's interpretation of Bohr's quantisation, the circumference of the $n^\text{th}$ stable orbit of the hydrogen atom must equal

1. de Broglie (1923) argued that the orbiting electron must be treated as a particle wave — and only those orbits would persist that support STANDING waves. 2. A standing wave around a closed loop of circumference $C$ requires $C = n\lambda$, where $\lambda$ is the de Broglie wavelength. 3. For the $n^\text{th}$ Bohr orbit, $C = 2\pi r_n$, so $2\pi r_n = n\lambda$. 4. Using $\lambda = h/p = h/(m v_n)$ recovers Bohr's quantisation $m v_n r_n = nh/(2\pi)$. So Bohr's once-mysterious second postulate is just the standing-wave condition for the electron's matter wave. 5. This is the elegant unification de Broglie produced ten years after Bohr. 6. Options B–D mix up wavelengths and length scales that have no role in this derivation. _Source: NCERT Class 12 Physics Part 2, Ch 12, §12.6 (De Broglie's Explanation of Bohr's Second Postulate, Eq. 12.12 + Fig. 12.8), p. 11–12._