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

Atomic orbitals are regions of space around an atom's nucleus where an electron is most likely to be found, and they follow a certain organization based on the principal quantum number (n), angular momentum quantum number (l), and magnetic quantum number (m). Each atomic orbital has a specific notation, where the principal quantum number is followed by a letter designating the subshell (s, p, d, or f) and sometimes also the magnetic quantum number. Now, let's understand the notation of an atomic orbital: 1. The principal quantum number (n) determines the energy level of the orbital and must be a positive integer (1, 2, 3, ...). Greater values of n indicate higher energy levels. 2. The angular momentum quantum number (l) determines the shape of the orbital and can have integer values ranging from 0 to (n-1). 3. The magnetic quantum number (m) determines the orientation of the orbital in space and can have integer values ranging from -l to +l. The letter designations for the subshells are as follows: 0 = s 1 = p 2 = d 3 = f

For a certain principal quantum number (n), we can identify the possible subshells with the help of the angular momentum quantum number (l). For example: - For n = 1, l can only be 0, so there is only one subshell (1s) available. - For n = 2, l can be 0 or 1, so there are two subshells (2s and 2p) available. - For n = 3, l can be 0, 1, or 2, so there are three subshells (3s, 3p, and 3d) available.

A hydrogen atom has only one electron bound to a single proton in its nucleus. This means that the hydrogen atom can populate only one atomic orbital. Now we need to determine if a hydrogen atom can have a 3s orbital.

The given statement mentions a 3s orbital. This indicates a principal quantum number (n) of 3 and an angular momentum quantum number (l) of 0 (since s refers to l=0). This combination is possible as per the rules of quantum numbers. However, as mentioned earlier, a hydrogen atom has only one electron. The electron will occupy the lowest available energy level, which, in this case, would be the 1s orbital. A hydrogen atom in its ground state (lowest energy state) cannot have a populated 3s orbital, as its only electron is in the 1s orbital. However, if the hydrogen atom were to absorb energy and reach an excited state, it could temporarily have its electron in the 3s orbital.

Based on our analysis of hydrogen's electronic configuration and understanding of atomic orbitals, we can conclude that the given statement can be considered "true" when referring to a hydrogen atom in an excited state. However, in the context of a hydrogen atom in its ground state, the statement would be false. To provide a concise answer: The statement is conditionally true. A hydrogen atom can have a 3s orbital only when it is in an excited state.