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# The number of radial nodes and angular nodes for d-orbital can be represented as:(a) \$(n - 2)\$radial nodes + 1 angular node = \$(n - 1)\$total nodes(b)\$(n - 1)\$radial nodes + 1 angular node = \$(n - 1)\$ total nodes(c) \$(n - 3)\$radial nodes + 2 angular nodes = \$(n - l - 1)\$total nodes(d) \$(n - 3)\$radial nodes + 2 angular nodes = \$(n - 1)\$ total nodes

Last updated date: 12th Sep 2024
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Hint: The nodes in an orbital are the points where the probability of finding an electron is zero. The total number of nodes is given by \$(n - 1)\$, the number of radial nodes by \$(n - l - 1)\$ and the number of angular nodes by \$l\$ . Here n is the principal quantum number and it denotes the shells while l is the azimuthal quantum number which describes the orbital angular momentum for an atomic orbital and describes the shape of the orbital.

1: As we know the total number of nodes is given by \$(n - 1)\$, where \$n\$ is the principal quantum number.
2: \$l\$ is the Azimuthal quantum number, which describes the shape of orbitals. The value of \$l\$ can be from 0 to \$(n - 1)\$ . The values describe a shape, so 0 is for s-orbital, 1 for p-orbital and 2 for d-orbital and so on.
3: Here, we have to calculate the number of radial and angular nodes. So,
Number of angular nodes = \$l\$
Here, for d-orbital, \$l\$ = 2.
∴ Number of angular nodes = 2
4: For radial nodes, the formula is: total nodes – angular nodes
\$ = (n - 1) - l\$
Putting the values of \$n\$ and \$l\$ in the formula, we get: