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  • 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

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 :

Option: 1

n^{2}


Option: 2

n


Option: 3

n^{\frac{1}{2}}


Option: 4

n^{\frac{1}{4}}


Answers (1)

\begin{aligned} &q v B=\frac{m v^{2}}{r} ; m v r=\frac{n h}{2 \pi}\\ &\therefore \frac{q B r}{m}=\frac{n h}{2 \pi m r}\\ &\therefore r \propto n^{1 / 2} \end{aligned}

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Kshitij

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