Imagine a Universe in which the four quantum numbers can have the same possible value as in our Universe except that the magnetic quantum number (m) can have integral values from 0 to `pm (l + 1)`.
Find the electronic configuration of atomic number 20. 

Options

A. `1s^6 2s^6 2p^8`
B. `1s^2 2s^2 2p^6 3s^2 3p^6 4s^2`
C. `1s^4 2s^4 2p^6 3s^4 3p^2`
D. `1s^2,1p^6 2s^2 1s^10`

Answer

To find the electronic configuration of an atom with atomic number 20, we will follow the principles of filling electrons into orbitals based on the quantum numbers and the modified rules given in the question. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Atomic Number
The atomic number (Z) of the element is given as 20. This means the element has 20 electrons.

### Step 2: Determine the Order of Filling Orbitals
In our universe, electrons fill orbitals in the order of increasing energy levels according to the Aufbau principle. The order of filling is generally:
1. 1s
2. 2s
3. 2p
4. 3s
5. 3p
6. 4s
7. 3d
8. 4p
9. 5s
10. 4d
11. 5p
12. 6s
13. 4f
14. 5d
15. 6p
16. 7s
17. 5f
18. 6d
19. 7p

### Step 3: Fill the Orbitals
We will fill the orbitals according to the modified magnetic quantum number rule, but since the values of m are still limited by l, we can proceed as follows:

1. **1s**: Can hold 2 electrons → 1s²
2. **2s**: Can hold 2 electrons → 2s²
3. **2p**: Can hold 6 electrons → 2p⁶
4. **3s**: Can hold 2 electrons → 3s²
5. **3p**: Can hold 6 electrons → 3p⁶
6. **4s**: Can hold 2 electrons → 4s²

### Step 4: Count the Electrons
Now, let's count the electrons filled:
- 1s² = 2
- 2s² = 2
- 2p⁶ = 6
- 3s² = 2
- 3p⁶ = 6
- 4s² = 2

Total = 2 + 2 + 6 + 2 + 6 + 2 = 20 electrons.

### Step 5: Write the Final Electronic Configuration
The electronic configuration for the element with atomic number 20 (Calcium) is:
**1s² 2s² 2p⁶ 3s² 3p⁶ 4s²**

### Summary
Thus, the electronic configuration of atomic number 20 is:
**1s² 2s² 2p⁶ 3s² 3p⁶ 4s²**

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