What is the total number of nodes present in the atomic orbitals that are occupied by electrons in the atom of Zn?

A. 11

B. 15

C. 16

D. 25

To determine the total number of nodes present in the atomic orbitals occupied by electrons in a zinc (Zn) atom, we first need to understand what nodes are and how they relate to the electron configuration of the atom. Nodes are regions in an atomic orbital where the probability of finding an electron is zero. There are two types of nodes: radial nodes and angular nodes. The total number of nodes in an orbital can be calculated using the formula: total nodes = n - 1, where n is the principal quantum number of the orbital. Additionally, the number of angular nodes is equal to the azimuthal quantum number (l).

Electron Configuration of Zinc

Zinc has an atomic number of 30, which means it has 30 electrons. The electron configuration for zinc can be written as:

• 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰

This configuration indicates that the electrons occupy the following orbitals:

• 1s: 2 electrons
• 2s: 2 electrons
• 2p: 6 electrons
• 3s: 2 electrons
• 3p: 6 electrons
• 4s: 2 electrons
• 3d: 10 electrons

Calculating Nodes for Each Orbital

Now, let's calculate the total number of nodes for each occupied orbital:

• 1s (n=1, l=0): Total nodes = 1 - 1 = 0 nodes (0 angular nodes)
• 2s (n=2, l=0): Total nodes = 2 - 1 = 1 node (0 angular nodes, 1 radial node)
• 2p (n=2, l=1): Total nodes = 2 - 1 = 1 node (1 angular node, 0 radial nodes)
• 3s (n=3, l=0): Total nodes = 3 - 1 = 2 nodes (0 angular nodes, 2 radial nodes)
• 3p (n=3, l=1): Total nodes = 3 - 1 = 2 nodes (1 angular node, 1 radial node)
• 4s (n=4, l=0): Total nodes = 4 - 1 = 3 nodes (0 angular nodes, 3 radial nodes)
• 3d (n=3, l=2): Total nodes = 3 - 1 = 2 nodes (2 angular nodes, 0 radial nodes)

Summing Up the Nodes

Now, let's add up all the nodes from the occupied orbitals:

• 1s: 0 nodes
• 2s: 1 node
• 2p: 1 node
• 3s: 2 nodes
• 3p: 2 nodes
• 4s: 3 nodes
• 3d: 2 nodes

Calculating the total:

• Total nodes = 0 + 1 + 1 + 2 + 2 + 3 + 2 = 11 nodes

Final Answer

Therefore, the total number of nodes present in the atomic orbitals occupied by electrons in a zinc atom is 11. The correct answer is A. 11.