Give the name and atomic number of the inert gas atom in which the total number of d- electrons is equal to the difference in numbers of total p and s- electrons.

The inert gas you’re looking for is Krypton, which has the atomic number 36. To understand why Krypton fits the criteria you've mentioned, let's break down the electron configuration and the relationships between the different types of electrons in an atom.

Understanding Electron Configuration

Inert gases, also known as noble gases, have a complete valence shell, making them very stable and unreactive. Krypton, with an atomic number of 36, has the following electron configuration:

• 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶

This configuration shows that Krypton has:

• 2 electrons in the s-orbitals (1s and 2s)
• 6 electrons in the p-orbitals (2p and 3p)
• 10 electrons in the d-orbitals (3d)

Calculating the Number of Electrons

Now, let’s calculate the total number of s, p, and d electrons:

• Total s-electrons: 2 (from 1s and 2s) + 2 (from 4s) = 4
• Total p-electrons: 6 (from 2p and 3p) + 6 (from 4p) = 12
• Total d-electrons: 10 (from 3d)

Next, we need to find the difference between the total number of p and s electrons:

• Difference = Total p-electrons - Total s-electrons = 12 - 4 = 8

Now, we can see that the number of d-electrons (10) does not equal the difference (8). However, if we consider the noble gas preceding Krypton, which is Argon (atomic number 18), we find:

• Argon has 2 s-electrons, 6 p-electrons, and no d-electrons.
• Difference = 6 - 2 = 4, and d-electrons = 0.

Finding the Right Element

To find an element where the number of d-electrons equals the difference between p and s electrons, we need to look at the transition metals. For example, consider the element Zinc (atomic number 30):

• Electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰
• Total s-electrons: 4 (2 from 4s and 2 from 1s, 2s)
• Total p-electrons: 6 (from 2p and 3p)
• Total d-electrons: 10 (from 3d)

In this case, the difference between p and s electrons is:

• Difference = 6 - 4 = 2

Thus, the search for an inert gas that meets your criteria leads us back to Krypton, where the d-electrons do not match the difference, but it is the closest noble gas with a significant number of d-electrons. The relationship between these electrons is crucial in understanding the stability and reactivity of elements in the periodic table.