Question

The wave function ${\psi }_{n,l,m}$ is a mathematical function whose value depends upon spherical polar coordinates $(r,\theta ,\varphi )$ of the electron and characterized by the quantum numbers n, l and $m_l$. Here r is distance from nucleus, $\theta$ is colatitude and $\varphi$ is azimuth. In the mathematical functions given in the table, Z is atomic number and $a_0$ is Bohr radius.

For the given orbital in Column-I, the only CORRECT combination for any hydrogen-like species is:

• A. (IV) (iv) (R)
• B. (II) (ii) (P)
• C. (III) (iii) (P)
• D. (I) (ii) (S)

Answer 1

The correct option is B (II) (ii) (P)

Number of radial nodes = $(n-l-1)$

Along the radius is a spherical node

Number of angular nodes = $l$

So for a 2s orbital,

Number of radial nodes = $(2-0-1)=1$

So the wavefunction of 2s has one radial node and the graph of the wave function vs radius is given below, with one point where the wavefuction changes from +ve to -ve.