Chemistry - Atomic Structure Question with Solution | TestHub

ChemistryAtomic StructureSchrödinger's EquationMedium2 minQB

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Passage / Comprehension

The wave function for an atomic orbital of single electron atom or ion is $ψ (r, θ, ϕ) = \frac{2}{3} (\frac{Z}{3 a _{0}})^{3/2} (1 - σ) (12 - 8 σ + σ^{2}) \cdot σ \cdot e^{- σ /2} \cdot cos θ$ . where $σ = \frac{2 Zr}{na _{0}}$ and $a_{0} =$ $0.529 \overset{˚}{A}$ . All other parameters have their usual meaning.

Read the following statements related with the given atomic orbital : (i) It has 2 radial nodes. (ii) It has 1 angular node. (iii) The total number of nodal surfaces are 4. (iv) The radial wave function changes its sign three times in $ψ (r)$ vs r curve. (v) The given orbital may be $6 p_{z}$ . The number of correct statement is :

Options:

Answer:

Solution:

Angular Node: The $cos θ$ dependency means $l = 1$ , giving 1 angular node.

Radial Nodes: Solving $(1 - σ) (σ^{2} - 8 σ + 12) = 0$ gives 3 positive roots (radial nodes).

Total Nodes: Total nodal surfaces equal $3 + 1 = 4$ .

Sign Changes: A function with 3 radial nodes changes sign 3 times.

Conclusion: Statements (ii), (iii), and (iv) are correct (Option B).

Stream:JEESubject:ChemistryTopic:Atomic StructureSubtopic:Schrödinger's Equation

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