Question

the coefficient of atomic orbitals in sp2 hybrid orbital is​

Answer 1

Explanation:

They are hybridized atomic orbitals formed by mixing s and p orbitals, to describe bonding in molecules.

Explanation:

In an sp3 hybridization, one s orbital is mixed with three p orbitals to form four sp3 hybridized orbitals. Each of these hybridized orbitals have 25% s character and 75% p character (calculated according to the proportion of s:p mixing). These sp3 hybridized orbitals are oriented with bond angle of 109.5 degrees to minimize electron repulsion, in a tetrahedral geometry. An example of sp3 hybridization can be seen in the carbons in ethane.

In an sp2 hybridization, one s orbital is mixed with two p orbitals to form three sp2 hybridized orbitals. Each of these hybridized orbitals have 33% s character and 67% p character. These sp2 hybridized orbitals are oriented with bond angle of 120 degrees, in a trigonal planar (triangular) geometry. The remaining p orbital is unchanged and perpendicular to the plane of the hybridized orbitals. An example of sp2 hybridization can be seen in the carbons in ethene.

In an sp hybridization, one s orbital is mixed with one p orbitals to form two sp hybridized orbitals. Each of these hybridized orbitals have 50% s character and 50% p character. These sp hybridized orbitals are oriented with bond angle of 180 degrees, in a linear geometry. The remaining two p orbitals are unchanged, and perpendicular to each other and the plane of the hybridized orbitals. An example of sp hybridization can be seen in the carbons in ethyne.

The mixing of orbitals can be seen here:

Hybridization - Wikimedia Commons

Orientation of the hybridized orbitals in respective geometries:



Answer 2

Answer:

The coefficient of atomic orbitals in sp² hybrid orbital is​ $\frac{1}{\sqrt{2} }$

Explanation:

Due to the overlapping of one s- and two p- orbitals three sp² hybridized orbitals are formed.

Ψ₁ = a₁Ψ₀ + b₁Ψpₓ + c₁Ψpₐ  .................................(1)

Ψ₂ = a₂Ψ₀ + b₂Ψpₓ + c₂Ψpₐ  ..............................(2)

Ψ₃ = a₃Ψ₀ + b₃Ψpₓ + c₃Ψpₐ  ..............................(3)

Here, a₁, a₂, a₃, b₁, b₂, b₃, c₁, c₂ and c₃ = Linear combination coefficients or mixing coefficients.

a₁² + a₂² + a₃² = $\frac{1}{3}$  ..............................................(4)

a₁ = a₂ = a₃ =  $\frac{1}{\sqrt{3} }$   ..............................................(5)

Where Ψ₁ is a normalized wave function, therefore

a₁² + b₁² + c₁² = 1

a₁² + b₁² = 1  .........................................................(6)

a₁= $\frac{1}{\sqrt{3} }$    ................................................................(7)

$\frac{1}{3}$ +  b₁² = 1

b₁² = $\frac{2}{3}$          Where  b₁ = $\sqrt{\frac{2}{3} }$ .......................(8)

Ψ₁ , Ψ₂ and Ψ₁ , Ψ₃ are orthogonal

∫Ψ₁ , Ψ₂ dτ = 0    and  ∫Ψ₁ , Ψ₃ dτ = 0  

According to the concept of orthogonality

a₁a₂ + b₁b₂ = 0   ...........................................(9)

a₁a₃ + b₁b₃ = 0    ..........................................(10)

b₂ = -$\frac{a_{1}a_{2} }{b_{1} }$ = $\frac{(1/\sqrt{3}) (1/\sqrt{3}) }{\sqrt{2/3} } = - \frac{1}{\sqrt{6} }$      ..............(11)

b₃ = -$\frac{a_{1} a_{3} }{b_{1} } = \frac{(1/\sqrt{3)}( 1/\sqrt{3} }{\sqrt{\frac{2}{3} } } = - \frac{1}{\sqrt{6} }$  ...................(12)

Ψ₂ is normalized wave function

∫Ψ₂² dτ  = 1

a₂² + b₂² + c₂² = 1

c₂² = 1 - ( a₂² + b₂²)  ..............................(13)

Substituting the values of a₂ and b₂ in above equation

c₂² = 1- $(\frac{1}{3} + \frac{1}{6})$

c₂ = $\frac{1}{\sqrt{2} }$  .......................................(14)

Ψ₃ is normalized wave function

∫Ψ₃² dτ  = 1

a₃³ + b₃³ + c₃³ = 1

c₃³ = 1 - (a₃³ + b₃³)

c₃³ =  $1 - (\frac{1}{3} + \frac{1}{6} )$    = $\frac{1}{2}$

c₃ = ±$\frac{1}{\sqrt{2} }$

The coefficient of atomic orbitals in sp² hybrid orbital is​ $\frac{1}{\sqrt{2} }$

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