The ratio of angular momentum L to the atomic dipole moment μ _ i...

The ratio of angular momentum

L

to the atomic dipole moment

{μ}_{i}

for hydrogen like atoms and ions is The ratio of angular momentum L to the atomic dipole moment μ _ i for hydrogen like atoms and ions is

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Aalways constant and is equal to the ratio of mass to the charge of electron
Balways constant and is equal to twice the ratio of mass to the charge of electron to the principal quantum number $n$
Cproportional to the principal quantum number $n$
Dproportional to $\dfrac{1}{n2}$

A. always constant and is equal to the ratio of mass to the charge of electron

The electron moving with a speed $v$ in the circular Bohr orbit of radius $r$ constitutes a current of magnitude.

The ratio of angular momentum L to the atomic dipole moment μ _ i for hydrogen like atoms and ions is

$i = \dfrac{e}{T}.$ where $T$ is the orbital period of the electron.

$T = 2\pir / v$

$i = \dfrac{ev}{2\pir}$

By definition of atomic dipole moment ${μ}_{i},$ its magnitude is given by

${μ}_{i} = iA = \dfrac{eV}{2\pir} \cdot \pir^{2} = \dfrac{evr}{2}$

$∴$ Angular momentum, $L = mvr$
$∴ \dfrac{L}{\mui} = \dfrac{2mvr}{evr} = \dfrac{2m}{e} = \text{constant}$