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. The hydrogen atom can have an electron in the 3s orbital (n=3, l=0) when it is in an excited state, having absorbed energy to transition from the ground state to this higher energy level. However, it's important to note that the electron is typically found in the ground state (1s orbital) when the atom has not absorbed sufficient energy for the transition.

Step-by-step solution

Recall of quantum numbers and orbitals

In order to address this question, we must first understand the basic concept of orbitals and their notations in an atom. There are four quantum numbers (n, l, m_l, and m_s) that define the properties of electrons in atoms. The principal quantum number (n) indicates the energy level of the electron and can take on positive integer values (1, 2, 3, ...). The azimuthal quantum number (l) defines the orbital shape and can range from 0 to (n-1). Finally, the magnetic quantum number (m_l) defines the orientation of the orbital in space and can take on integer values ranging from -l to +l. Orbitals are regions in space where the probability of finding an electron is high. They are represented by notations like "3s" which combine the value of the principal quantum number (n) and the orbital type (s, p, d, or f) defined by the azimuthal quantum number (l), where l = 0 (s), 1 (p), 2 (d), or 3 (f).

Identifying the hydrogen atom's orbitals

The hydrogen atom has only one electron. Therefore, according to the quantum numbers mentioned above, the hydrogen atom can have various electron configurations in higher energy levels. The orbital being discussed in this question is "3s", which refers to an orbital with the principal quantum number n=3 and the azimuthal quantum number l=0 (s).

Evaluating the statement

Based on our understanding of orbitals and quantum numbers, the statement "The hydrogen atom has a 3s orbital" is true. This is because the hydrogen atom can have an electron in the 3s orbital, which is higher in energy than the ground state (1s) orbital. When the hydrogen atom's electron is in the 3s orbital, it is in an excited state, as it has absorbed energy to move from the ground state to this higher energy level. So, it's important to note that the electron may not always be found in the 3s orbital but rather in the ground state most of the time, when the atom has not absorbed the energy required for the transition.