The angular momentum of electron revolving in the second...

The angular momentum of electron revolving in the second orbit of $\mathrm{H}$ -atom is ' $x^{\prime} \mathrm{J} \cdot \mathrm{s}$. The angular momentum of electron in the second orbit of $\mathrm{He}^{+}$ ion should be (a) $x \mathrm{~J} \cdot \mathrm{s}$ (b) $2 x \mathrm{~J} \cdot \mathrm{s}$ (c) $0.5 x \mathrm{~J} \cdot \mathrm{s}$ (d) $4 x \mathrm{~J} \cdot \mathrm{s}$

The angular momentum of electron revolving in the second orbit of $\mathrm{H}$ -atom is ' $x^{\prime} \mathrm{J} \cdot \mathrm{s}$. The angular momentum of electron in the second orbit of $\mathrm{He}^{+}$ ion should be
(a) $x \mathrm{~J} \cdot \mathrm{s}$
(b) $2 x \mathrm{~J} \cdot \mathrm{s}$
(c) $0.5 x \mathrm{~J} \cdot \mathrm{s}$
(d) $4 x \mathrm{~J} \cdot \mathrm{s}$

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Key Concepts

Quantization of Angular Momentum

According to the Bohr model, the angular momentum of an electron in any orbit is quantized and is given by L = n(h/2?), where n is the principal quantum number. This quantization rule applies universally to any hydrogen-like atom, meaning that for a given energy level, the angular momentum remains the same regardless of the nuclear charge.

Hydrogen-like Atoms

Hydrogen-like atoms are ions that have only one electron, such as He+. Their electron dynamics are analogous to the electron in a hydrogen atom, following the same quantized formulas for energy levels and angular momentum. However, while the energy levels and radii scale with the nuclear charge, the quantized angular momentum (n(h/2?)) remains independent of the nuclear charge.

Bohr Model

The Bohr model describes the electron in an atom as moving in circular orbits around the nucleus, with certain allowed radii corresponding to fixed energy levels. It introduces the idea that only specific quantized orbits are permitted, where the electron’s energy and orbital radius depend principally on the principal quantum number n.

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