Write down electronic configuration of chromium `(Z=24)` and indicate in it.
(i) numbers of sub-shells
(ii) number of orbitals
(iii) number of electrons in M-shell

Answer

To solve the question, we will follow these steps:

### Step 1: Write the Electronic Configuration of Chromium (Z=24)
The electronic configuration of chromium can be determined by filling the orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. For chromium, the electronic configuration is:

\[ \text{Cr: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \]

### Step 2: Identify the Number of Sub-shells
In the electronic configuration of chromium, we can identify the different sub-shells:
- 1s
- 2s
- 2p
- 3s
- 3p
- 4s
- 3d

Counting these, we find that there are **7 sub-shells**.

### Step 3: Determine the Number of Orbitals
Next, we will count the number of orbitals in each sub-shell:
- The s sub-shell has **1 orbital** (1s, 2s, 3s, 4s)
- The p sub-shell has **3 orbitals** (2p, 3p)
- The d sub-shell has **5 orbitals** (3d)

Now, let's add them up:
- Total orbitals = 1 (from 1s) + 1 (from 2s) + 3 (from 2p) + 1 (from 3s) + 3 (from 3p) + 1 (from 4s) + 5 (from 3d) = **15 orbitals**.

### Step 4: Calculate the Number of Electrons in the M-shell
The M-shell corresponds to the principal quantum number \( n = 3 \). The electrons in the M-shell come from the 3s, 3p, and 3d sub-shells:
- 3s: 2 electrons
- 3p: 6 electrons
- 3d: 5 electrons

Adding these together gives us:
- Total electrons in M-shell = 2 + 6 + 5 = **13 electrons**.

### Final Summary
- Electronic Configuration of Chromium: \( 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^1 \, 3d^5 \)
- Number of Sub-shells: **7**
- Number of Orbitals: **15**
- Number of Electrons in M-shell: **13**

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