For a single-electron species, the plot of radial probability density ^2 against the distance from the nucleus r exhibits a non-zero maximum at r=0 . Furthermore, the curve touches the r -axis at exactly two distinct points before asymptotically approaching zero. Which of the following atomic orbitals does this plot represent?

Step-by-step solution

The radial probability density ^2 has a non-zero maximum at the nucleus ( r=0 ). This is a characteristic feature of s-orbitals, so the azimuthal quantum number l = 0 . The curve touches the r -axis at exactly two distinct points, which means there are 2 radial nodes. The number of radial nodes is given by the formula n - l - 1 . Equating this to 2, we get: n - 0 - 1 = 2 n = 3 Therefore, the principal quantum number is n = 3 and the orbital is 3s. Answer: 3s