JEE Main 2020 · 5 September · evening · Single correct · +4 / −1
The correct statement about probability density (except at infinite distance from nucleus) is :
- (a) It can be zero for 1s orbital
- (b) It can be zero for 3p orbital
- (c) It can never be zero for 2s orbital
- (d) It can negative for 2p orbital
Answer and solution
Answer (b) It can be zero for 3p orbital
Solution
Chemistry ma’am · 3 steps
Probability density is ψ²: it can drop to zero at a node, but it can never go negative.
- What density is. Probability density is ψ², the square of the wave function. A square can be zero but never negative, and it is zero exactly where ψ = 0, that is, at a node.
- Count the nodes. An orbital has n - l - 1 radial nodes (spheres) and l angular nodes (planes or cones). If either count is non-zero, the density is zero somewhere at a finite distance.
Orbital Radial nodes n-l-1 Angular nodes l Can ψ² be zero? 1s 1-0-1 = 0 0 No 2s 2-0-1 = 1 0 Yes, on one spherical node 2p 2-1-1 = 0 1 Yes, on the nodal plane, but never negative 3p 3-1-1 = 1 1 Yes, on the spherical node and the nodal plane - So. The 3p orbital has two nodes, so its probability density can be zero. The correct statement is (b).
The idea to keep. The sign belongs to ψ, not to ψ². For zero density, look for nodes: n-l-1 radial plus l angular. Only 1s has no node at all.
Answer from the NTA final answer key. Solution by PrepWiser.