7.2.3 Angular Solutions to the Schrödinger Equation Flashcards
Angular Solutions to the Schrödinger Equation
- The solutions to Schrödinger’s equation have both a radial and an angular component.
- The angular solutions describe the shape of the electron orbital; the p orbitals have directionality and one nodal plane.
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- The solutions to Schrödinger’s equation have both a radial and angular component.
- The solutions for the s orbitals were derived by holding the angular part of the equation constant and provide information only about the probability of the presence of an electron at a given distance from the nucleus; s orbitals are spherical in shape.
- The angular solutions to Schrödinger’s equation describe the shape of the electron orbital.
- The example shows the equation for one of three p orbitals. When theta ( ) is 90°, cos = 0 and the probability of finding the electron is zero. Thus the electron is forbidden in the x-y plane (for the p z orbital). This is the single angular node characteristic of the p orbitals. Similar solutions are obtained for the other two p orbitals.
- The p orbitals have directionality, and the probability function describes a probability “cloud” of a specific shape in three-dimensional space.
- The d orbitals and f orbitals have two and three angular
nodes respectively, giving them different shapes than the p orbitals.
How many angular nodes does a p orbital have?
1
The angular wave function for a 2pz orbital depends on which of the following values?
θ, the angle between a point and the z-axis
Which of the following statements does not describe a 2py orbital?
It has a node along the y-axis.
Suppose that the radial part of a wave function was equal to 1. What effect would this have on the orbital?
The probability of finding an electron would remain the same as the distance from the nucleus increased.
Which of the following orbitals has three spherical nodes, no planar nodes, and lacks directionality?
4s
How is an angular node different from a radial node?
An angular node has only two dimensions, but a radial node has three.
The angular wave function for a 2px orbital is shown below.
(3/4π)^1/2 (sin θ) (cos φ)
Where will this orbital have a node?
where sine θ or cosine φ is equal to 0
Which of the following is the best description of the radial portion of a 2pz orbital?
It has no radial nodes; in any given direction, the probability of finding an electron decreases exponentially as the distance from the nucleus increases.
For which of the following sets of spherical coordinates (r, θ, φ) would the probability of finding an electron in a 2pz orbital be zero? (Assume that θ is the angle between the point and the z-axis and that φ is the angle between the x-axis and a projection of the point onto the xy-plane.)
(0.2 angstrom, 90°, 5°)
What is the probability of finding a particular electron above the yz-plane in a 2px orbital?
50%