The orbital pair having same number of
spherical nodes is
(A) 2p, 3s
(B) 3p, 5d
(C) 4f, 5s
(D) 3s, 5d
Answers
Answer:
A) 2p, 3s
Explanation:
please add as brilliant answer
Answer:
Explanation:There are multiple orbitals within an atom. Each has its own specific energy level and properties. Because each orbital is different, they are assigned specific quantum numbers: 1s, 2s, 2p 3s, 3p,4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. The numbers, (n=1,2,3, etc.) are called principal quantum numbers and can only be positive numbers. The letters (s,p,d,f) represent the orbital angular momentum quantum number (ℓ) and the orbital angular momentum quantum number may be 0 or a positive number, but can never be greater than n-1. Each letter is paired with a specific ℓ value:
s: subshell = 0
p: subshell = 1
d: subshell = 2
f: subshell = 3
An orbital is also described by its magnetic quantum number (mℓ). The magnetic quantum number can range from –ℓ to +ℓ. This number indicates how many orbitals there are and thus how many electrons can reside in each atom.
Orbitals that have the same or identical energy levels are referred to as degenerate. An example is the 2p orbital: 2px has the same energy level as 2py. This concept becomes more important when dealing with molecular orbitals. The Pauli exclusion principle states that no two electrons can have the same exact orbital configuration; in other words, the same quantum numbers. However, the electron can exist in spin up (ms = +1/2) or with spin down (ms = -1/2) configurations. This means that the s orbital can contain up to two electrons, the p orbital can contain up to six electrons, the d orbital can contain up to 10 electrons, and the f orbital can contain up to 14 electrons.
s subshell p subshell d subshell f subshell
Table 1: Breakdown and Properties of Subshells
ℓ = 0 ℓ = 1 ℓ = 2 ℓ = 3
mℓ = 0 mℓ= -1, 0, +1 mℓ= -2, -1, 0, +1, +2 mℓ= -3, -2, -1, 0, +1, +2, +3
One s orbital Three p orbitals Five d orbitals Seven f orbitals
2 s orbital electrons 6 p orbital electrons 10 d orbital electrons 14 f orbital electrons
Visualizing Electron Orbitals
As discussed in the previous section, the magnetic quantum number (ml) can range from –l to +l. The number of possible values is the number of lobes (orbitals) there are in the s, p, d, and f subshells. As shown in Table 1, the s subshell has one lobe, the p subshell has three lobes, the d subshell has five lobes, and the f subshell has seven lobes. Each of these lobes is labeled differently and is named depending on which plane the lobe is resting in. If the lobe lies along the x plane, then it is labeled with an x, as in 2px. If the lobe lies along the xy plane, then it is labeled with a xy such as dxy. Electrons are found within the lobes. The plane (or planes) that the orbitals do not fill are called nodes. These are regions in which there is a 0 probability density of finding electrons. For example, in the dyx orbital, there are nodes on planes xz and yz. This can be seen in Figure 12.9.1 .
Single_electron_orbitals.jpg
Figure 12.9.1 : The 1s orbital (red), the 2p orbitals (yellow), the 3d orbitals (blue) and the 4f orbitals (green) are contrasted.
Radial and Angular Nodes
There are two types of nodes, angular and radial nodes. Angular nodes are typically flat plane (at fixed angles), like those in the diagram above. The ℓ quantum number determines the number of angular nodes in an orbital. Radial nodes are spheres (at fixed radius) that occurs as the principal quantum number increases. The total nodes of an orbital is the sum of angular and radial nodes and is given in terms of the n and l quantum number by the following equation:
N=n−l−1(12.9.1)
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Figure 12.9.2 : Two orbitals. (left) The 3px orbital has one radial node and one angular node. (right) The 5dxz orbital has two radial nodes and two angular nodes. Images used with permission from Wikipedia
For example, determine the nodes in the 3pz orbital, given that n = 3 and ℓ = 1 (because it is a p orbital). The total number of nodes present in this orbital is equal to n-1. In this case, 3-1=2, so there are 2 total nodes. The quantum number ℓ determines the number of angular nodes; there is 1 angular node, specifically on the xy plane because this is a pz orbital. Because there is one node left, there must be one radial node. To sum up, the 3pz orbital has 2 nodes: 1 angular node and 1 radial node. This is demonstrated in Figure 2.
Another example is the 5dxy orbital. There are four nodes total (5-1=4) and there are two angular nodes (d orbital has a quantum number ℓ=2) on the xz and zy planes. This means there there must be two radial nodes. The number of radial and angular nodes can only be calculated if the principal quantum number, type of orbital (s,p,d,f), and the plane that the orbital is resting on (x,y,z, xy, etc.) are known.