7.2.3 Angular Solutions to the Schrödinger Equation Flashcards Preview

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Flashcards in 7.2.3 Angular Solutions to the Schrödinger Equation Deck (12)
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1
Q

Angular Solutions to the Schrödinger Equation

A
  • 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.
2
Q

note

A
  • 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.
3
Q

How many angular nodes does a p orbital have?

A

1

4
Q

The angular wave function for a 2pz orbital depends on which of the following values?

A

θ, the angle between a point and the z-axis

5
Q

Which of the following statements does not describe a 2py orbital?

A

It has a node along the y-axis.

6
Q

Suppose that the radial part of a wave function was equal to 1. What effect would this have on the orbital?

A

The probability of finding an electron would remain the same as the distance from the nucleus increased.

7
Q

Which of the following orbitals has three spherical nodes, no planar nodes, and lacks directionality?

A

4s

8
Q

How is an angular node different from a radial node?

A

An angular node has only two dimensions, but a radial node has three.

9
Q

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?

A

where sine θ or cosine φ is equal to 0

10
Q

Which of the following is the best description of the radial portion of a 2pz orbital?

A

It has no radial nodes; in any given direction, the probability of finding an electron decreases exponentially as the distance from the nucleus increases.

11
Q

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.)

A

(0.2 angstrom, 90°, 5°)

12
Q

What is the probability of finding a particular electron above the yz-plane in a 2px orbital?

A

50%

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