Question

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms? a. The principal quantum number completely determines the energy of a given electron. b. The angular momentum quantum number, \(\ell,\) determines the shapes of the atomic orbitals. c. The magnetic quantum number, \(m_{\ell},\) determines the direction that the atomic orbitals point in space.

Short answer

Answer: a. True for the hydrogen atom only. b. True for all atoms. c. True for all atoms.

Step-by-step solution

Statement a

The principal quantum number completely determines the energy of a given electron. For the hydrogen atom, the energy of an electron is solely determined by the principal quantum number, \(n\). However, for multi-electron systems, the energy depends on both the principal quantum number, \(n\), and the angular momentum quantum number, \(\ell\). Therefore, this statement is: Answer: True for the hydrogen atom only.

Statement b

The angular momentum quantum number, \(\ell,\) determines the shapes of the atomic orbitals. The shapes of atomic orbitals are determined by the value of the angular momentum quantum number, \(\ell\). This is an essential principle of atomic structure, and it holds true for all atoms, not just the hydrogen atom. Therefore, this statement is: Answer: True for all atoms.

Statement c

The magnetic quantum number, \(m_{\ell},\) determines the direction that the atomic orbitals point in space. The magnetic quantum number, \(m_{\ell},\) is responsible for determining the orientation of atomic orbitals in space. It is an essential property of atomic orbitals that holds true for all atoms, not just the hydrogen atom. Thus, this statement is: Answer: True for all atoms.