`X^(+),Y^(2+)and Z` are isoelectronic with `CO_(2)` . Increasing order of protons in `X^(+),Y^(2+)` and Z is :

Options

A. (a)`X^(+)=Y^(2+)=Z`
B. (b)`X^(+)ltY^(2+)ltZ`
C. (c)`ZltX^(+)ltY^(2+)`
D. (d)`Y^(2+)ltX^(+)ltZ`

Answer

To solve the problem, we need to determine the increasing order of protons in the ions \(X^+\), \(Y^{2+}\), and \(Z\) that are isoelectronic with \(CO_2\). Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the number of electrons in \(CO_2\)
- Carbon has 6 electrons, and each oxygen has 8 electrons. Since there are 2 oxygen atoms:
\[ \text{Total electrons in } CO_2 = 6 + 8 + 8 = 22 \text{ electrons} \]

### Step 2: Understand the meaning of isoelectronic species
- Isoelectronic species have the same number of electrons. Since \(X^+\), \(Y^{2+}\), and \(Z\) are isoelectronic with \(CO_2\), they also have 22 electrons.

### Step 3: Calculate the atomic number (number of protons) for each species
- For \(X^+\):
- It has a positive charge, meaning it has lost one electron. Therefore, the number of protons (atomic number) must be:
\[ \text{Atomic number of } X = 22 + 1 = 23 \]

- For \(Y^{2+}\):
- It has a +2 charge, meaning it has lost two electrons. Therefore, the number of protons (atomic number) must be:
\[ \text{Atomic number of } Y = 22 + 2 = 24 \]

- For \(Z\):
- It is neutral and has the same number of electrons as protons. Therefore, the atomic number is:
\[ \text{Atomic number of } Z = 22 \]

### Step 4: List the atomic numbers (number of protons)
- \(X^+\): 23 protons
- \(Y^{2+}\): 24 protons
- \(Z\): 22 protons

### Step 5: Arrange the atomic numbers in increasing order
- The increasing order of protons is:
\[ Z (22) < X^+ (23) < Y^{2+} (24) \]

### Final Answer
The increasing order of protons in \(X^+\), \(Y^{2+}\), and \(Z\) is:
\[ Z < X^+ < Y^{2+} \]