The radial probability distribution curve (plot of 4 r^2 R^2 versus r ) for a particular atomic orbital of a hydrogen-like species exhibits exactly 3 peaks. If this orbital possesses exactly 1 angular node, what is its designation?

Step-by-step solution

The number of angular nodes for an orbital is equal to its azimuthal quantum number l . Since the orbital has 1 angular node, l = 1 , which corresponds to a p-orbital. For a radial probability distribution curve ( 4 r^2 R^2 versus r ), the number of peaks is equal to n - l . Given that the curve has 3 peaks, we have: n - l = 3 Substituting l = 1 into the equation: n - 1 = 3 n = 4 Thus, the principal quantum number is n = 4 and the azimuthal quantum number is l = 1 . The orbital is designated as 4p. Answer: 4p