Atomic StructuremediumNUMERICAL

In a hydrogen-like atom, the circumference of the Bohr orbit is observed to be exactly times the de Atomic Structure Chemistry Question

Question

In a hydrogen-like atom, the circumference of the $n^{\text{th}}$ Bohr orbit is observed to be exactly $4$ times the de Broglie wavelength of the electron revolving in that orbit. Find the value of the principal quantum number $n$.

Answer: 4

💡 Solution & Explanation

According to de Broglie's wave theory applied to Bohr's orbits, an electron forms a stationary standing wave along the circumference of the orbit. This condition is given by $2\pi r = n\lambda$. The problem states that the circumference $2\pi r = 4\lambda$. Equating the two expressions gives $n = 4$.

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