Mr. Santa has to decode a number "ABCDEF", where each alphabet is represented by a single digit. Suppose an orbital whose radial wave function is represented as ψ ( r ) = k 1 ⋅ e − τ / k 2 ( r 2

Question

Mr. Santa has to decode a number "ABCDEF", where each alphabet is represented by a single digit. Suppose an orbital whose radial wave function is represented as $ψ_{(r)} = k_{1} \cdot e^{- τ / k_{2}} (r^{2} - 5 k_{3} r + 6 k_{3}^{2})$ .

From the following information given about each alphabet, write down the answers in the form of (A+B+C+D+E+F) for the above orbital.

Info A = Value of $n$ , where " $n$ " is the principal quantum number.

Info B = Number of angular nodes.

Info C = Azimuthal quantum number of the subshell to which the orbital belongs.

Info D = Number of subshells having energy between $(n + 5) s$ to $(n + 5) p$ , where $n$ is the principal quantum number (assuming energy depends both on $n$ and $ℓ$ ).

Info E = Orbital angular momentum of the given orbital.

Info F = Radial distance of the spherical node which is farthest from the nucleus

(assuming $k_{3} = 1$ ).

TestHub · Accepted Answer

Number of radial nodes = n − ℓ − 1 = 2 Number of Angular nodes = 0 ​ n = 3 ⇒ A = 3 , B = 0 , C = 0 ( n + 5 ) s = 8 s ( n + 5 ) p = 8 p E = ℓ ( ℓ + 1 ) ​ 2 π h ​ = 0 r 2 − 5 r + 6 = 0 r 2 − 2 r − 3 r + 6 = 0 r ( r − 2 ) − 3 ( r − 2 ) = 0 ( r − 2 ) ( r − 3 ) = 0 F = 3 A + B + C + D + E + F = 3 + 0 + 0 + 3 + 0 + 3 = 9 ​

Chemistry - Atomic Structure Question with Solution | TestHub

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JEE Advanced 2027 (Class 12)