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Point out the anugular momentum of an el...

Point out the anugular momentum of an electron in,
(a) `4s` orbital (b) `3p` orbital (c ) `4^(th)` orbit )according to Bohr model)

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To find the angular momentum of an electron in different orbitals, we can use the following principles: ### Step-by-Step Solution: 1. **Understanding Angular Momentum in Quantum Mechanics**: The angular momentum \( L \) of an electron in an orbital can be calculated using the formula: \[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \] where \( l \) is the azimuthal quantum number and \( h \) is Planck's constant. 2. **(a) Angular Momentum of an Electron in the `4s` Orbital**: - For the `s` orbital, the azimuthal quantum number \( l = 0 \). - Therefore, the angular momentum \( L \) is: \[ L = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} = 0 \] - **Result**: The angular momentum of an electron in the `4s` orbital is **0**. 3. **(b) Angular Momentum of an Electron in the `3p` Orbital**: - For the `p` orbital, the azimuthal quantum number \( l = 1 \). - Therefore, the angular momentum \( L \) is: \[ L = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \] - **Result**: The angular momentum of an electron in the `3p` orbital is \( \frac{h \sqrt{2}}{2\pi} \). 4. **(c) Angular Momentum of an Electron in the `4th` Orbit (Bohr Model)**: - According to the Bohr model, the angular momentum \( L \) of an electron in the \( n^{th} \) orbit is given by: \[ L = n \cdot \frac{h}{2\pi} \] - For the 4th orbit (\( n = 4 \)): \[ L = 4 \cdot \frac{h}{2\pi} = \frac{4h}{2\pi} = \frac{2h}{\pi} \] - **Result**: The angular momentum of an electron in the `4th` orbit is \( \frac{2h}{\pi} \). ### Summary of Results: - (a) Angular momentum in `4s` orbital: **0** - (b) Angular momentum in `3p` orbital: \( \frac{h \sqrt{2}}{2\pi} \) - (c) Angular momentum in `4th` orbit: \( \frac{2h}{\pi} \)

To find the angular momentum of an electron in different orbitals, we can use the following principles: ### Step-by-Step Solution: 1. **Understanding Angular Momentum in Quantum Mechanics**: The angular momentum \( L \) of an electron in an orbital can be calculated using the formula: \[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} ...
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