Question #44266

An electron in a hydrogenic ion is excited to a stationary state characterized by the wavefunction $\psi(r, \theta, \phi)$. Analysis of the probability density $|\psi|^2$ reveals exactly one radial (spherical) node and zero electron density on the mutually perpendicular planes defined by the equations $x = 0$ and $z = 0$. Assuming the standard quantum mechanical convention mapping real $d$-orbitals to magnetic quantum numbers ($m_l = 0$ for $d_{z^2}$, $m_l = \pm 1$ for $d_{xz}, d_{yz}$, and $m_l = \pm 2$ for $d_{xy}, d_{x^2-y^2}$), which of the following correctly identifies the principal, azimuthal, and magnetic quantum numbers $(n, l, m_l)$ for this state, along with the geometric axis where its planar nodes intersect?