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# Maximum number of nodes is present in:(A)$5s$ (B)$5p$(C)$5d$(D)All have same number of nodes

Last updated date: 22nd Jul 2024
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Hint: The number of nodes is one less than the principal quantum number. The principal quantum number is used to describe the energy of an electron and also the most probable distance of an electron from the nucleus. It is represented by$n$.

The number of nodes is the difference of principal quantum number and one. It is given by the following formula: ${\text{Number of nodes = Principal quantum number - 1}}$. Now find the number of nodes for all the given options.
$5s \to {\text{Number of nodes = 5 - 1 = 4}}$
$5p \to {\text{Number of nodes = 5 - 1 = 4}}$
$5d \to {\text{Number of nodes = 5 - 1 = 4}}$
Note that the number of nodes depends on the principal quantum number. As all have the same principal quantum number, they all will have the same number of nodes too.

Therefore, option D is the correct answer.

The total number of nodes in an orbital is equal to the difference of principal quantum number and 1. The number of radial nodes is given by$n - l - 1$. The number of angular nodes is equal to$l$. Here, $n$is the principal quantum number and $l$ is the azimuthal quantum number.