Chapter 3: Problem 50

Hydrogen's only electron occupies the 1\(s\) orbital but can be excited to a 4\(p\) orbital. List all of the orbitals that this electron can occupy as it "falls."

Short Answer

Expert verified

The full list of transitions for the electron 'falling' from the excited 4p state to the ground 1s state, in order, is: 4p -> 3d -> 4s -> 3p -> 3s -> 2p -> 2s -> 1s.

Step by step solution

Identifying energy levels and orbitals

Firstly, it's important to understand the energy levels of electrons in an atom and what these orbitals mean. A hydrogen atom's electron configuration starts with the \(1s\) orbital, which is the lowest energy level and is closest to the nucleus. After the \(1s\) orbital, the energy levels increase and the orbitals are filled in the following order: \(2s, 2p, 3s, 3p, 4s, 3d, 4p\). The number corresponds to the principal quantum number (n) which indicates the 'energy level'. The letter represents the shape of the orbital (spherical for 's', dumbbell-shaped for 'p', etc.)

Listing the transitions

Now that we understand the hierarchy of energy levels, we're ready to list all possible transitions for a hydrogen electron falling from the 4p level to 1s. According to the electron configuration hierarchy: \(4p -> 3d -> 4s -> 3p -> 3s -> 2p -> 2s -> 1s\)

Arranging in order

Rearranging these transitions in orderly sequence as the electron 'falls' down the energy levels gives us the following walkthrough: From its excited state in 4p, the electron can fall to 3d, then to 4s, then to 3p, then to 3s, then to 2p, then to 2s, and finally to its ground state in 1s, completing its transition.

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Hydrogen's only electron occupies the 1\(s\) orbital but can be excited to a 4\(p\) orbital. List all of the orbitals that this electron can occupy as it "falls."

Short Answer

Step by step solution

Identifying energy levels and orbitals

Listing the transitions

Arranging in order

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