For a particular atomic orbital, the plot of the radial wavefunction ( ) versus the distance from the nucleus ( r ) crosses the horizontal axis exactly twice. If the subshell to which this orbital belongs can accommodate a maximum of 10 electrons, what is the principal quantum number ( n ) of the orbital?

Step-by-step solution

The maximum number of electrons a subshell can accommodate is given by 4l + 2 . Given that the subshell can hold a maximum of 10 electrons: 4l + 2 = 10 4l = 8 l = 2 . This corresponds to a d-subshell. The number of times the versus r plot crosses the horizontal axis (excluding the origin and infinity) is equal to the number of radial nodes. Given that the plot crosses the axis twice, the number of radial nodes is 2 . The formula for the number of radial nodes is n - l - 1 . Substituting the known values: n - 2 - 1