Explain the difference between the probability density distribution for an orbital and its radial probability.

Short Answer

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The probability density distribution for an orbital is a 3D function that measures the probability of finding an electron at a specific location (r, θ, and φ) in the space around the nucleus of an atom. On the other hand, the radial probability is a 1D function that represents the probability of finding the electron at a certain distance (r) from the nucleus, regardless of its angular position (θ and φ). The radial probability can be obtained by integrating the probability density distribution over all possible angles at a given radial distance.

Step by step solution

01

Define Probability Density Distribution for an Orbital

The probability density distribution for an orbital, also known as the electron probability density function, is a measure of the probability of finding an electron in a specific location within the 3D space around the nucleus of an atom. It is a function of three variables: the distance from the nucleus (r), and the two angles (θ and φ) defining the position in spherical coordinates.
02

Define Radial Probability

The radial probability of an electron in an atom is the probability of finding the electron at a certain distance (r) from the nucleus, regardless of its angular position (θ and φ). It is a function of the distance r alone and can be obtained by integrating the probability density distribution over all possible angles.
03

Compare and Contrast Probability Density Distribution for an Orbital and Radial Probability

Both probability density distribution for an orbital and radial probability are related to the electron's distribution in an atom. However, there are differences between the two: 1. Variables: The probability density distribution is a function of three variables (r, θ, and φ) representing the position of the electron in 3D space, while the radial probability is a function of only the distance (r) from the nucleus. 2. Dimension: The probability density distribution for an orbital gives a 3D picture of the electron's distribution in an atom, while the radial probability gives a 1D representation of the electron's distribution along the radial direction. 3. Integration: To obtain the radial probability from the probability density distribution, one must integrate the probability density function over all possible angles (θ and φ) at a given distance (r) from the nucleus.
04

Summary

The probability density distribution for an orbital and its radial probability both describe the electron's distribution in an atom. The former is a 3D function that provides information on the probability of finding an electron at a specific location in the space around the nucleus, while the latter is a 1D representation of the electron's distribution along the radial direction. To obtain the radial probability, the probability density distribution needs to be integrated over all possible angles at a given radial distance.

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