What is the exact de Broglie wavelength associated with an electron revolving in the Bohr orbit of a — Atomic Structure Chemistry Question

💡 Solution & Explanation

According to Bohr's quantization condition and de Broglie's wave theory, an electron in the $n^{th}$ orbit forms a standing wave such that $2\pi r_n = n\lambda$. For the $3^{rd}$ orbit of hydrogen, $n = 3$ and $r_3 = 3^2 a_0 = 9a_0$. Substituting these values, $2\pi(9a_0) = 3\lambda$, which simplifies to $\lambda = 6\pi a_0$.