Question

How many nodes are there in the 1s 2p and 3d orbitals ? How many nodes are in a 4f orbital?

Answer 1

Hint: Node is the specified area or space present in the atomic orbital which has negligible electron density. In other words, the area present in an orbital having zero probability of electrons is known as nodes . The number of nodes depends upon the value of the principal quantum number. The principal quantum number is denoted by $n$ .

Complete answer:
The number of nodes is given by $n - l - 1$ nodes, where $n$ is the value of the principal quantum number and $l$ is the orbital angular momentum quantum number . For $1s$ Number of nodes in $1s$ orbital is given by $n - l - 1$ Value of principal quantum number $n$ = $1$ Value of orbital angular momentum quantum number $l$ = $0$ So the number of nodes $ = 1 - 0 - 1$ $ \Rightarrow 0$ nodes For $2p$ Number of nodes in $2p$ orbital is given by $n - l - 1$ Value of principal quantum number $n$ = $2$ Value of orbital angular momentum quantum number $l$ = $1$ So the number of nodes $ = 2 - 1 - 1$ $ \Rightarrow 0$ nodes For $3d$ Number of nodes in $3d$ orbital is given by $n - l - 1$ Value of principal quantum number $n$ = $3$ Value of orbital angular momentum quantum number $l$ = $2$ So the number of nodes $ = 3 - 2 - 1$ $ \Rightarrow 0$ nodes For $4f$ Number of nodes in $4f$ orbital is given by $n - l - 1$ Value of principal quantum number $n$ = $4$ Value of orbital angular momentum quantum number $l$ = $3$ So the number of nodes $ = 4 - 3 - 1$ $ \Rightarrow 0$ nodes
Note:
 Never confuse the principal quantum number and angular momentum quantum number . The number of nodes is given by $n - l - 1$ nodes, where $n$ is the value of the principal quantum number and $l$ is the orbital angular momentum quantum number . $s,p,d$ and $f$ are the subshell of a shell. These subshells represent the electron density of an atom .