100 pm in front of the nucleus, along the -y axis. 100 pm to the left of the nucleus, along the -x axis.

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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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## Position Comparison Relative to the Nucleus

This table compares the positions of two points, A and B, relative to a nucleus in a coordinate system. 

### Points and Coordinates:

- **Point A**: 
  - 100 pm in front of the nucleus, along the -y axis.
  - 100 pm above the nucleus, along the +z axis.
  - 100 pm below the nucleus, along the -z axis.

- **Point B**: 
  - 100 pm to the left of the nucleus, along the -x axis.
  - 100 pm to the right of the nucleus, along the +x axis.
  - 100 pm behind the nucleus, along the +y axis.

### Comparison of \( P_A \) to \( P_B \):

1. **For the coordinates on the first row**:
   - **Point A**: 100 pm in front of the nucleus, along the -y axis.
   - **Point B**: 100 pm to the left of the nucleus, along the -x axis.
   - **Comparison**: \(P_A < P_B\) (marked with an 'O')

2. **For the coordinates on the second row**:
   - **Point A**: 100 pm above the nucleus, along the +z axis.
   - **Point B**: 100 pm to the right of the nucleus, along the +x axis.
   - **Comparison**: \(P_A < P_B\) (marked with an 'O')

3. **For the coordinates on the third row**:
   - **Point A**: 100 pm below the nucleus along the -z axis.
   - **Point B**: 100 pm behind the nucleus, along the +y axis.
   - **Comparison**: \(P_A < P_B\) (marked with an 'O')

These comparisons illustrate the relative positions of points A and B in a three-dimensional space surrounding a nucleus.
Transcribed Image Text:## Position Comparison Relative to the Nucleus This table compares the positions of two points, A and B, relative to a nucleus in a coordinate system. ### Points and Coordinates: - **Point A**: - 100 pm in front of the nucleus, along the -y axis. - 100 pm above the nucleus, along the +z axis. - 100 pm below the nucleus, along the -z axis. - **Point B**: - 100 pm to the left of the nucleus, along the -x axis. - 100 pm to the right of the nucleus, along the +x axis. - 100 pm behind the nucleus, along the +y axis. ### Comparison of \( P_A \) to \( P_B \): 1. **For the coordinates on the first row**: - **Point A**: 100 pm in front of the nucleus, along the -y axis. - **Point B**: 100 pm to the left of the nucleus, along the -x axis. - **Comparison**: \(P_A < P_B\) (marked with an 'O') 2. **For the coordinates on the second row**: - **Point A**: 100 pm above the nucleus, along the +z axis. - **Point B**: 100 pm to the right of the nucleus, along the +x axis. - **Comparison**: \(P_A < P_B\) (marked with an 'O') 3. **For the coordinates on the third row**: - **Point A**: 100 pm below the nucleus along the -z axis. - **Point B**: 100 pm behind the nucleus, along the +y axis. - **Comparison**: \(P_A < P_B\) (marked with an 'O') These comparisons illustrate the relative positions of points A and B in a three-dimensional space surrounding a nucleus.
### 2p_y Orbital Visualization and Electron Probability Analysis

#### Sketch of a 2p\(_y\) Orbital:
Below is a sketch representing a 2p\(_y\) atomic orbital. This sketch is approximately 800 picometers (pm) wide. The coordinate axes (x, y, and z) are also depicted to provide spatial context. 

![2p_y Orbital Sketch](insert_image_url_here)

*Figure 1: Representation of a 2p\(_y\) orbital with coordinate axes.*

You can rotate the sketch for a better view of the orbital by dragging the slider with your mouse.

#### Understanding Probability in Orbitals:
Let's consider an atom with its nucleus positioned at the origin. This atom has an electron in a 2p\(_y\) orbital. We are interested in comparing the probability of locating the electron at different points, specifically points \(A\) and \(B\).

The table below helps in analyzing how the probability \(P_A\) (finding the electron at point A) compares with \(P_B\) (finding the electron at point B).

| Point A | Point B | Compare \(P_A\) to \(P_B\) |
|---------|---------|----------------------------|
|         |         | \(\leq P_B\)               |

*Table 1: Comparative probability of finding an electron at points A and B.*

### Instructions:
1. **Interactive Component**: Use the slider beneath the sketch to rotate and examine the 2p\(_y\) orbital from different angles.
2. **Probability Analysis**: Use the knowledge of the orbital shape and node presence to determine and compare probabilities of electron location at various points.

This exercise aims to enhance your understanding of electron distribution within atomic orbitals and the factors influencing probability density.
Transcribed Image Text:### 2p_y Orbital Visualization and Electron Probability Analysis #### Sketch of a 2p\(_y\) Orbital: Below is a sketch representing a 2p\(_y\) atomic orbital. This sketch is approximately 800 picometers (pm) wide. The coordinate axes (x, y, and z) are also depicted to provide spatial context. ![2p_y Orbital Sketch](insert_image_url_here) *Figure 1: Representation of a 2p\(_y\) orbital with coordinate axes.* You can rotate the sketch for a better view of the orbital by dragging the slider with your mouse. #### Understanding Probability in Orbitals: Let's consider an atom with its nucleus positioned at the origin. This atom has an electron in a 2p\(_y\) orbital. We are interested in comparing the probability of locating the electron at different points, specifically points \(A\) and \(B\). The table below helps in analyzing how the probability \(P_A\) (finding the electron at point A) compares with \(P_B\) (finding the electron at point B). | Point A | Point B | Compare \(P_A\) to \(P_B\) | |---------|---------|----------------------------| | | | \(\leq P_B\) | *Table 1: Comparative probability of finding an electron at points A and B.* ### Instructions: 1. **Interactive Component**: Use the slider beneath the sketch to rotate and examine the 2p\(_y\) orbital from different angles. 2. **Probability Analysis**: Use the knowledge of the orbital shape and node presence to determine and compare probabilities of electron location at various points. This exercise aims to enhance your understanding of electron distribution within atomic orbitals and the factors influencing probability density.
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