First slide

Hydrogen -like ion

Question

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 nth orbital will therefore be proportional to

Moderate

A

n²
B

n
C

n^3/2
D

n^1/2

Solution

Given that $2 πr = nλ; 2 πr = n \frac{h}{mV}$
$and BqV = \frac{{mV}^{2}}{r}; r = \frac{mV}{Bq} mV = Bqr; 2 πr = n \frac{h}{Bqr} \Rightarrow r^{2} \propto n \Rightarrow r \propto n^{1 / 2}$

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