The electronic configuration of an element is `1s^(2) 2s^(2) 2p^(6)3s^(2) 3p^(6) 4s^(2) 3d^(10) 4p^(2)` . What is the atomic number of the element which is just below the above element in the poriodic table ?

Options

A. 36
B. 49
C. 50
D. 54

Answer

To find the atomic number of the element just below the one with the given electronic configuration, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Electronic Configuration:**
The electronic configuration provided is:
\[ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2 \]

2. **Calculate the Atomic Number:**
To find the atomic number, we need to sum the electrons in each subshell:
- \(1s^2\) contributes 2 electrons
- \(2s^2\) contributes 2 electrons
- \(2p^6\) contributes 6 electrons
- \(3s^2\) contributes 2 electrons
- \(3p^6\) contributes 6 electrons
- \(4s^2\) contributes 2 electrons
- \(3d^{10}\) contributes 10 electrons
- \(4p^2\) contributes 2 electrons

Now, let's sum these:
\[ 2 + 2 + 6 + 2 + 6 + 2 + 10 + 2 = 32 \]
Therefore, the atomic number of the element is 32.

3. **Identify the Element:**
The element with atomic number 32 is Germanium (Ge).

4. **Determine the Element Below Germanium:**
The element just below Germanium in the periodic table is found in the same group (Group 14) but in the next period (Period 5). The electronic configuration for the element below Germanium (Tin, Sn) is:
\[ [Kr] 5s^2 4d^{10} 5p^2 \]

5. **Calculate the Atomic Number of the Element Below:**
Now, we will calculate the atomic number of Tin:
- The configuration can be broken down as follows:
- \(5s^2\) contributes 2 electrons
- \(4d^{10}\) contributes 10 electrons
- \(5p^2\) contributes 2 electrons

Summing these:
\[ 2 + 10 + 2 = 14 \]
Adding this to the noble gas core (\(Kr\), which has an atomic number of 36):
\[ 36 + 14 = 50 \]
Therefore, the atomic number of the element just below Germanium is 50.

6. **Conclusion:**
The atomic number of the element just below Germanium in the periodic table is **50**, which corresponds to Tin (Sn).