Suppose an orbital of a hydrogen-like atom is represented, with its radial wave function as given below and its angular function as 2 π 1 . ψ ( r ) = k 1 . e k 2 − r ( r 2 − 5 k 3 r + 6 k

Question

Suppose an orbital of a hydrogen-like atom is represented, with its radial wave function as given below and its angular function as $\frac{1}{2 π}$ .

$ψ (r) = k_{1} . e^{\frac{- r}{k _{2}}} (r^{2} - 5 k_{3} r + 6 k_{3}^{2})$

Find the value of $(A + B + C + D + E + F)$ , where:

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

B = Number of angular nodes.

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

D = Maximum number of subshells having energy more than $(n + 5) s$ and less than $(n + 5) p$ , where $n$ is the principal quantum number.

E = Orbital angular momentum of the given orbital.

F = Radial distance of the spherical node (in Å) which is farthest from the nucleus

(assuming $k_{3} = 1$ Unit and $r$ values are measured in Å).

TestHub · Accepted Answer

Orbital is 3 s ⇒ ℓ = 0 and polynomial is of order 2 ⇒ n = ℓ − 1 = 2 or n = 3 ( A = 3 , B = 0 , C = 0 , D = 3 , E = 0 , F = 3 )

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