The `Ew` of an element is `13`. It forms an acidic oxide which `KOH` forms a salt isomorphous with `K_(2)SO_(4)`. The `Aw` of element is
a. `13`, b. `26`, c. `52`, d. `78`

Options

A. 13
B. 26
C. 52
D. 78

Explanation

To solve the problem, we need to determine the atomic weight (Aw) of the element based on the given equivalence weight (Ew) and the information about the acidic oxide and the salt formed with KOH.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- The equivalence weight (Ew) of the element is given as 13.
- The element forms an acidic oxide.
- The salt formed with KOH is isomorphous with K₂SO₄.

2. **Identifying the Valency:**
- Since the salt formed is isomorphous with K₂SO₄, we can infer that the valency of the element (let's denote it as 'M') should be the same as the valency of sulfur (S) in sulfate (SO₄²⁻).
- The valency of sulfur in K₂SO₄ is 6 (since the sulfate ion has a charge of -2 and there are 2 potassium ions, each with a +1 charge).

3. **Using the Relationship Between Atomic Weight and Equivalence Weight:**
- The relationship between atomic weight (Aw), equivalence weight (Ew), and valency (n) is given by the formula:
\[ \text{Aw} = \text{Ew} \times n \]
- Here, we have:
\[ \text{Aw} = 13 \times 6 \]

4. **Calculating the Atomic Weight:**
- Now, we can calculate the atomic weight:
\[ \text{Aw} = 13 \times 6 = 78 \]

5. **Conclusion:**
- Therefore, the atomic weight (Aw) of the element is 78.

### Final Answer:
The atomic weight (Aw) of the element is **78** (Option D).

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