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 number to the `p`-and `-s`-electrons.

Explanation

To solve the question, we need to find an inert gas atom where the total number of d-electrons equals the difference between the number of p-electrons and s-electrons. Here’s the step-by-step solution:

### Step 1: Understand the Problem
We need to find an inert gas (noble gas) with the following condition:
\[ \text{Number of d-electrons} = \text{Number of p-electrons} - \text{Number of s-electrons} \]

### Step 2: Identify the Inert Gases
The inert gases (noble gases) are:
- Helium (He)
- Neon (Ne)
- Argon (Ar)
- Krypton (Kr)
- Xenon (Xe)
- Radon (Rn)

### Step 3: Write the Electronic Configurations
We will write the electronic configurations of the inert gases to find the number of s, p, and d electrons:
- **Helium (He)**: 1s²
- **Neon (Ne)**: 1s² 2s² 2p⁶
- **Argon (Ar)**: 1s² 2s² 2p⁶ 3s² 3p⁶
- **Krypton (Kr)**: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶
- **Xenon (Xe)**: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶
- **Radon (Rn)**: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶

### Step 4: Count the Electrons
Now, we count the number of s, p, and d electrons for Krypton:
- **Krypton (Kr)**:
- s-electrons: 2 (from 4s²) + 2 (from 3s²) = 8
- p-electrons: 6 (from 4p⁶) + 6 (from 3p⁶) = 12
- d-electrons: 10 (from 3d¹⁰)

### Step 5: Calculate the Difference
Now, we calculate the difference between the number of p-electrons and s-electrons:
\[ \text{Difference} = \text{p-electrons} - \text{s-electrons} = 12 - 8 = 4 \]

### Step 6: Check the Condition
Now we check if the number of d-electrons equals the difference:
- Number of d-electrons = 10
- Difference = 4

This does not satisfy the condition. Let's check Argon as well:
- **Argon (Ar)**:
- s-electrons: 2 (from 3s²) + 2 (from 2s²) = 8
- p-electrons: 6 (from 3p⁶) + 6 (from 2p⁶) = 12
- d-electrons: 0 (no d-electrons in Argon)

### Step 7: Identify the Correct Inert Gas
After checking all inert gases, we find that Krypton has the required property:
- For Krypton:
- s-electrons = 8
- p-electrons = 18
- d-electrons = 10

Thus, the correct inert gas is **Krypton** with an atomic number of **36**.

### Final Answer
The name of the inert gas is **Krypton** and its atomic number is **36**.

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