Consider the orbital wave function, r (r,0,0) = A = A (za₁-4) 20₁² r ∙e 200 cos where A is some normalization constant and ao is the Bohr Radius (also a constant). (a) Consider the radial part of this function. For what values of r is it zero? How many radial nodes does this function have (points where the radial part is zero when r IS NOT equal to 0 or ∞o)? (b) Consider the angular part of this function. For what value of 0 or is it zero? How many angular nodes does this function have? (c) By using the general eigenfunction expression for the z-component of angular momentum, L₂(r,0,0) = m₂ħ(r, 0, 0) What is the value of my in this particular case. (d) By considering nodes and my, identify this orbital.
Consider the orbital wave function, r (r,0,0) = A = A (za₁-4) 20₁² r ∙e 200 cos where A is some normalization constant and ao is the Bohr Radius (also a constant). (a) Consider the radial part of this function. For what values of r is it zero? How many radial nodes does this function have (points where the radial part is zero when r IS NOT equal to 0 or ∞o)? (b) Consider the angular part of this function. For what value of 0 or is it zero? How many angular nodes does this function have? (c) By using the general eigenfunction expression for the z-component of angular momentum, L₂(r,0,0) = m₂ħ(r, 0, 0) What is the value of my in this particular case. (d) By considering nodes and my, identify this orbital.
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![Consider the orbital wave function,
r
r
200
e
4 (r, 0, 4) = A (274) 20€ za cost
2ao
where A is some normalization constant and do is the Bohr Radius (also a constant).
(a) Consider the radial part of this function. For what values of r is it zero? How many radial nodes
does this function have (points where the radial part is zero when r IS NOT equal to 0 or ∞)?
(b) Consider the angular part of this function. For what value of 0 or is it zero? How many angular
nodes does this function have?
(c) By using the general eigenfunction expression for the z-component of angular momentum,
Î₂(r,0,0) = m₂ħ(r, 0, 0)
What is the value of my in this particular case.
(d) By considering nodes and m₁, identify this orbital.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c170825-78f9-4028-8dad-6d73bf0df651%2Fa76d78a7-7370-42eb-94d8-132aebfd51ee%2Fh24ibk_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the orbital wave function,
r
r
200
e
4 (r, 0, 4) = A (274) 20€ za cost
2ao
where A is some normalization constant and do is the Bohr Radius (also a constant).
(a) Consider the radial part of this function. For what values of r is it zero? How many radial nodes
does this function have (points where the radial part is zero when r IS NOT equal to 0 or ∞)?
(b) Consider the angular part of this function. For what value of 0 or is it zero? How many angular
nodes does this function have?
(c) By using the general eigenfunction expression for the z-component of angular momentum,
Î₂(r,0,0) = m₂ħ(r, 0, 0)
What is the value of my in this particular case.
(d) By considering nodes and m₁, identify this orbital.
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