Question

Is the following statement true or false? The hydrogen atom has a \(3 s\) orbital. Explain.

Short answer

The statement "The hydrogen atom has a \(3s\) orbital" is true, but only when the hydrogen atom's electron is in an excited state. The electron can occupy any orbital within an energy level when it absorbs energy. However, the \(3s\) orbital is not always occupied, as the electron ultimately returns to the ground state.

Step-by-step solution

Understand the structure of a hydrogen atom

A hydrogen atom is the simplest of all atoms, consisting of a single proton and a single electron. The electron occupies various energy levels and orbitals around the nucleus (the proton).

Review the Quantum Numbers

There are four quantum numbers that define the electron's orbitals: 1. Principal Quantum Number (n): Describes the energy level and size of the orbital. It can take integer values starting from 1. 2. Azimuthal Quantum Number (l): Describes the shape of the orbital and depends on the principal quantum number. It can take integer values from 0 to n-1. 3. Magnetic Quantum Number (mᵩ): Describes the orientation of the orbital in space and depends on the azimuthal quantum number. It can take integer values from -l to +l. 4. Spin Quantum Number (mₛ): Describes the electron's intrinsic angular momentum. It has two possible values, +1/2 or -1/2.

Analyze the given statement - Hydrogen atom having a 3s orbital

The statement suggests that the hydrogen atom has a \(3s\) orbital. Recalling the definition of quantum numbers: - The \(3s\) orbital implies that the principal quantum number (n) = 3 and the azimuthal quantum number (l) = 0. - However, a hydrogen atom has only one electron.

Validate the statement

A hydrogen atom's single electron can occupy any orbital within an energy level, depending on its energy state. When a hydrogen atom is in its ground state (lowest energy level), the electron resides in the \(1s\) orbital. However, if a hydrogen atom absorbs energy (e.g., through electromagnetic radiation), the electron can be excited to a higher energy level. Therefore, a hydrogen atom can have a \(3s\) orbital when its electron is in an excited state. However, these excited states are not stable, and the electron will eventually drop back down to the ground state, releasing energy in the process.

Conclusion

The statement "The hydrogen atom has a \(3s\) orbital" is true, but only when the hydrogen atom's electron is in an excited state. It is important to note that the electron ultimately returns to the ground state, and the \(3s\) orbital is not always occupied.