how to calculate the number of nodes of
a) s orbital
b)p orbital
c)d orbital
d)f orbital
what is the general formula. please explain with the help of four distinct examples.

Asked by Sayoni Maiti | 5th Jun, 2014, 10:03: AM

Expert Answer:

Nodes are the spaces where the probability of finding the electron is zero.

To find the number of nodes in an orbital is given as follows:

Number of angular nodes = l

Number of radial nodes = n – 1 – l

Total number of nodes = n – 1

Therefore, the formula n-l-1

There are two types of nodes that can occur; angular and radial nodes.

Radial nodes are the nodes that appear along the radius of atom while angular nodes are the nodes that appear along the plane of the angle. These two differ mathematically.

Radial node

It is a spherical surface where the probability of an electron being found is 0 and the probability density equals 0. They radiate like circles away from the nucleus.

Each atomic orbital will have n-l-1 radial nodes. So a 3p orbital has 3-1-1 = 1 radial node.

Angular node

It is a plane dividing wave functions by phase (dividing negative and positive)

An atomic orbital will have l angular nodes. So, an s-orbital has 0 angular node and p-orbital has 1 angular node, and so on.

where n is principal quantum number [n can be any positive integer (1, 2, 3, 4...)]; l is angular momentum quantum number [l can equal: 0, 1, 2, 3, 4...(n-1)]. Notation used for l are 0 = s; 1 = p; 2 = d; 3 = f).

Answered by Hanisha Vyas | 9th Jun, 2014, 11:24: AM

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