Chapter 8: Problem 72
Identify the orbital that has (a) two radial nodes and one angular node; (b) five radial nodes and zero angular nodes; (c) one radial node and four angular nodes.
Short Answer
Expert verified
The orbitals are: (a) 3p; (b) 5s; (c) 5f
Step by step solution
01
Identify the Orbital in case (a) two radial nodes and one angular node.
For this case, since there are two radial nodes and one angular node, the total number of nodes or 'n', will be the sum of these two giving 'n' = 3. Also, for one angular node, the orbital must be of 'p type' which is denoted as 'l = 1'. Therefore, the orbital can be identified as '3p'.
02
Identify the Orbital in case (b) five radial nodes and zero angular nodes.
For this case, since there are five radial nodes and zero angular nodes, the total number of nodes or 'n', will be the sum of these two giving 'n' = 5. And for zero angular nodes, the orbital must be of 's type' which is denoted as 'l = 0'. Therefore, the orbital can be identified as '5s'.
03
Identify the Orbital in case (c) one radial node and four angular nodes.
For this case, since there is one radial node and four angular nodes, the total number of nodes or 'n', will be sum of these two giving 'n' = 5. And for four angular nodes, the orbital must be of 'f type' which is denoted as 'l = 3'. Therefore, the orbital can be identified as '5f'.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Orbital Types
In chemistry, orbitals are regions around the nucleus of an atom where electrons are most likely to be found. Different types of orbitals exhibit unique shapes and orientations within the atom. They are typically categorized as s, p, d, and f orbitals.
Understanding these orbital types is vital in predicting how atoms bond and react with one another. You can visualize the shape of these orbitals as clouds representing the most likely locations where an electron can be found. This can help clarify why certain molecules have their specific shapes and properties.
- s-orbitals: These orbitals are spherical in shape and can be found in any energy level (n). Each energy level has one s-orbital.
- p-orbitals: Shaped like dumbbells, p-orbitals exist in sets of three and come in any energy level from n=2 and upwards.
- d-orbitals: These orbitals have a complex, cloverleaf shape and come in sets of five. They are present from energy level n=3 onwards.
- f-orbitals: With even more complex shapes than the d-orbitals, f-orbitals come in sets of seven and are found in energy levels starting from n=4.
Understanding these orbital types is vital in predicting how atoms bond and react with one another. You can visualize the shape of these orbitals as clouds representing the most likely locations where an electron can be found. This can help clarify why certain molecules have their specific shapes and properties.
Radial Nodes
Radial nodes are regions within atomic orbitals where the probability of finding an electron is exactly zero. These nodes appear as concentric spheres around the nucleus, where the electron density falls to zero. The number of radial nodes an orbital has is determined by subtracting the angular momentum quantum number, \( l \), from the principal quantum number, \( n \).
The formula is:
The formula is:
- Number of radial nodes = \( n - l - 1 \).
Angular Nodes
Angular nodes are planes or surfaces where the probability of finding an electron is zero. These are caused by the orbital's shape and the orientation of its lobes rather than its distance from the nucleus. For example, in p-orbitals, the angular nodes align with planes that bisect the dumbbell shapes, and they manifest as nodes along the axes in the Cartesian coordinate system.
- Number of angular nodes = \( l \), where \( l \) is the azimuthal quantum number.