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An orbital has only positive values of w...

An orbital has only positive values of wave function at all distances from the nucleus. Find the value of `(n+l)` for this orbital.

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To solve the problem, we need to determine the value of \( n + l \) for an orbital that has only positive values of the wave function at all distances from the nucleus. ### Step-by-Step Solution: 1. **Understanding the Wave Function**: The wave function \( \psi \) describes the probability amplitude of finding an electron in a given region of space. If the wave function is always positive, it indicates that there are no nodes (points where the wave function is zero) in the orbital. 2. **Identifying the Orbital**: The only orbital that has a wave function that is always positive and does not touch or cross the zero line is the 1s orbital. This is because the 1s orbital has a spherical shape and does not have any nodes. 3. **Quantum Numbers**: - The principal quantum number \( n \) for the 1s orbital is 1. - The azimuthal quantum number \( l \) for the 1s orbital is 0 (since s orbitals correspond to \( l = 0 \)). 4. **Calculating \( n + l \)**: \[ n + l = 1 + 0 = 1 \] 5. **Conclusion**: Therefore, the value of \( n + l \) for the orbital with only positive values of the wave function is 1. ### Final Answer: The value of \( n + l \) for this orbital is **1**.
To solve the problem, we need to determine the value of \( n + l \) for an orbital that has only positive values of the wave function at all distances from the nucleus. ### Step-by-Step Solution: 1. **Understanding the Wave Function**: The wave function \( \psi \) describes the probability amplitude of finding an electron in a given region of space. If the wave function is always positive, it indicates that there are no nodes (points where the wave function is zero) in the orbital. 2. **Identifying the Orbital**: The only orbital that has a wave function that is always positive and does not touch or cross the zero line is the 1s orbital. This is because the 1s orbital has a spherical shape and does not have any nodes. ...
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