JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{th}\) orbital will therefore be proportional to
- A \(n^2\)
- B \(n\)
- C \(n^{1/2}\)
- D \(n^{1/4}\)
Answer & Solution
Correct Answer
(C) \(n^{1/2}\)
Step-by-step Solution
Detailed explanation
According to the question, \(2 \pi r=n \lambda=\frac{n h}{p}=\frac{n h}{m v}\) or \(\operatorname{mvr}=\frac{\mathrm{nh}}{2 \pi}\) or \(\mathrm{mv}=\frac{\mathrm{nh}}{2 \pi \mathrm{r}}\) \(\mathrm{F}=\mathrm{qv}_{\mathrm{B}}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}\) or,…
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