If the wave function of electron for H -like species is given as follows : Ψ = 9 8 π 1 [ a 0 z ] 2 3 e − 2 σ σ ( 4 − σ ) . s i n θ . c o s Φ Where σ = na 0 2 Zr At r = 3a 0 , p

Question

If the wave function of electron for H -like species is given as follows :

$Ψ = \frac{1}{9 8 π} [\frac{z}{a _{0}}]^{\frac{3}{2}} e^{- \frac{σ}{2} σ (4 - σ) . s i n θ . c o s}$ Φ

Where $σ = \frac{2 Zr}{na _{0}}$

At r = 3a₀ , probability density is zero irrespective of value of θ and ϕ, then what should be the value of (x + y).

where x = azimuthal quantum number of given orbital, y = atomic number of H-like species.

TestHub · Accepted Answer

Given orbital is 3 P x ​ So x = ℓ = 1 For radial node σ = 4 ​ na 0 ​ 2 Zr ​ = 4 ​ ​ ​ Z = 2 × 3 a 0 ​ 4 × 3 × a 0 ​ ​ Z = 2

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