Handwritten worksheet on atomic structure with a table and formulas for calculating atomic properties.

Problem Analysis:

The task involves filling in a table based on the relationships between atomic number, mass number, number of protons, number of electrons, number of neutrons, and charge. The rules provided are:

1. Atomic number (Z) = Number of protons.
2. Mass number (A) = Number of protons + Number of neutrons.
3. Number of protons = Number of electrons (in a neutral atom).
4. Number of neutrons = Mass number - Atomic number.
5. Charge = Difference between the number of protons and electrons.

The table has some missing values, and we need to fill them in using these rules.

Table Breakdown:

The table is structured as follows:
- S. No.: Serial number.
- Atomic no.: Atomic number (Z).
- Mass no.: Mass number (A).
- No. of Protons: Number of protons.
- No. of Electrons: Number of electrons.
- No. of Neutrons: Number of neutrons.
- Charge: Charge of the ion.

Step-by-Step Solution:

#### Row 1:
- Atomic no.: 17
- Mass no.: 36
- No. of Protons: 17 (same as atomic number)
- No. of Electrons: 17 (neutral atom)
- No. of Neutrons: \( 36 - 17 = 19 \)
- Charge: \( 17 - 17 = 0 \)

#### Row 2:
- Atomic no.: 71
- Mass no.: 180
- No. of Protons: 71 (same as atomic number)
- No. of Electrons: 71 (neutral atom)
- No. of Neutrons: \( 180 - 71 = 109 \)
- Charge: \( 71 - 71 = 0 \)

#### Row 3:
- Atomic no.: 40
- Mass no.: 86
- No. of Protons: 40 (same as atomic number)
- No. of Electrons: 38 (charge is +2, so \( 40 - 38 = +2 \))
- No. of Neutrons: \( 86 - 40 = 46 \)
- Charge: +2 (given)

#### Row 4:
- Atomic no.: 92
- Mass no.: 238
- No. of Protons: 92 (same as atomic number)
- No. of Electrons: 86 (charge is +6, so \( 92 - 86 = +6 \))
- No. of Neutrons: \( 238 - 92 = 146 \)
- Charge: +6 (given)

#### Row 5:
- Atomic no.: 82
- Mass no.: 206
- No. of Protons: 82 (same as atomic number)
- No. of Electrons: 78 (charge is +4, so \( 82 - 78 = +4 \))
- No. of Neutrons: \( 206 - 82 = 124 \)
- Charge: +4 (given)

#### Row 6:
- No. of Protons: 34
- No. of Electrons: 36 (charge is -2, so \( 34 - 36 = -2 \))
- Atomic no.: 34 (same as number of protons)
- Mass no.: Not given, but we can infer it if needed.
- No. of Neutrons: Not given, but can be calculated if mass number is known.
- Charge: -2 (given)

#### Row 7:
- Mass no.: 113
- No. of Protons: 48
- No. of Electrons: 49 (charge is -1, so \( 48 - 49 = -1 \))
- Atomic no.: 48 (same as number of protons)
- No. of Neutrons: \( 113 - 48 = 65 \)
- Charge: -1 (given)

Filled Table:

| S. No. | Atomic no. | Mass no. | No. of Protons | No. of Electrons | No. of Neutrons | Charge |
|--------|------------|----------|----------------|------------------|------------------|--------|
| 1 | 17 | 36 | 17 | 17 | 19 | 0 |
| 2 | 71 | 180 | 71 | 71 | 109 | 0 |
| 3 | 40 | 86 | 40 | 38 | 46 | +2 |
| 4 | 92 | 238 | 92 | 86 | 146 | +6 |
| 5 | 82 | 206 | 82 | 78 | 124 | +4 |
| 6 | 34 | — | 34 | 36 | — | -2 |
| 7 | 48 | 113 | 48 | 49 | 65 | -1 |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{S. No.} & \text{Atomic no.} & \text{Mass no.} & \text{No. of Protons} & \text{No. of Electrons} & \text{No. of Neutrons} & \text{Charge} \\
\hline
1 & 17 & 36 & 17 & 17 & 19 & 0 \\
\hline
2 & 71 & 180 & 71 & 71 & 109 & 0 \\
\hline
3 & 40 & 86 & 40 & 38 & 46 & +2 \\
\hline
4 & 92 & 238 & 92 & 86 & 146 & +6 \\
\hline
5 & 82 & 206 & 82 & 78 & 124 & +4 \\
\hline
6 & 34 & — & 34 & 36 & — & -2 \\
\hline
7 & 48 & 113 & 48 & 49 & 65 & -1 \\
\hline
\end{array}
}
\]