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Predict which of the following statement...

Predict which of the following statements are true or false.
Angular momentum for 2p and 3p orbital is same.

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To determine whether the statement "Angular momentum for 2p and 3p orbital is the same" is true or false, we can follow these steps: ### Step 1: Understand Angular Momentum Angular momentum (L) in quantum mechanics is given by 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. ### Step 2: Identify the Azimuthal Quantum Number (L) The azimuthal quantum number \( L \) is determined by the type of orbital: - For a **p orbital**, \( L = 1 \). ### Step 3: Determine L for 2p and 3p Orbitals Both 2p and 3p orbitals are p orbitals: - For **2p**, \( L = 1 \). - For **3p**, \( L = 1 \). ### Step 4: Calculate Angular Momentum for Both Orbitals Since both orbitals have the same azimuthal quantum number: \[ L_{2p} = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \] \[ L_{3p} = \sqrt{1(1 + 1)} \cdot \frac{h}{2\pi} = \sqrt{2} \cdot \frac{h}{2\pi} \] ### Step 5: Conclusion Since both angular momentum values are equal, we conclude that: **The statement is true.** ### Summary of the Solution: - Angular momentum depends on the azimuthal quantum number \( L \). - Both 2p and 3p orbitals have \( L = 1 \). - Therefore, their angular momentum is the same.

To determine whether the statement "Angular momentum for 2p and 3p orbital is the same" is true or false, we can follow these steps: ### Step 1: Understand Angular Momentum Angular momentum (L) in quantum mechanics is given by 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. ### Step 2: Identify the Azimuthal Quantum Number (L) ...
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