The spin-only magn etic moment value of `B_2^(+)` species is __________` xx 10^(-2)` BM. (Nearest integer)
[Given : `sqrt3 = 1.73`]

Answer

To solve the problem of finding the spin-only magnetic moment value of the \( B_2^+ \) species, we will follow these steps:

### Step 1: Understand the Formula for Spin-Only Magnetic Moment
The formula for the spin-only magnetic moment (\( \mu \)) is given by:

\[ \mu = \sqrt{n(n + 2)} \]

where \( n \) is the number of unpaired electrons.

### Step 2: Determine the Electron Configuration of \( B_2^+ \)
The atomic number of boron (B) is 5. Therefore, the molecular formula \( B_2 \) has a total of 10 electrons. Since we are dealing with \( B_2^+ \), we need to remove one electron, leaving us with 9 electrons.

### Step 3: Fill the Molecular Orbitals
According to molecular orbital theory, the filling order for the first 10 electrons in \( B_2 \) is as follows:

1. \( \sigma_{1s} \) - 2 electrons
2. \( \sigma_{1s}^* \) - 2 electrons
3. \( \sigma_{2s} \) - 2 electrons
4. \( \sigma_{2s}^* \) - 0 electrons
5. \( \pi_{2p_x} \) - 2 electrons
6. \( \pi_{2p_y} \) - 2 electrons
7. \( \sigma_{2p_z} \) - 0 electrons

For \( B_2^+ \) (9 electrons), the filling will be:

1. \( \sigma_{1s} \) - 2 electrons
2. \( \sigma_{1s}^* \) - 2 electrons
3. \( \sigma_{2s} \) - 2 electrons
4. \( \sigma_{2s}^* \) - 0 electrons
5. \( \pi_{2p_x} \) - 2 electrons
6. \( \pi_{2p_y} \) - 1 electron (since we have 9 electrons total)

### Step 4: Count the Unpaired Electrons
From the filling, we see that in the \( \pi_{2p_x} \) and \( \pi_{2p_y} \) orbitals, there is one unpaired electron in \( \pi_{2p_y} \). Therefore, \( n = 1 \).

### Step 5: Calculate the Spin-Only Magnetic Moment
Now, substituting \( n = 1 \) into the formula:

\[ \mu = \sqrt{1(1 + 2)} = \sqrt{3} \]

### Step 6: Convert to the Required Units
The value of \( \sqrt{3} \) is approximately 1.73. Since the problem asks for the answer in \( \times 10^{-2} \) BM, we convert it:

\[ \mu = 1.73 \, \text{BM} = 173 \times 10^{-2} \, \text{BM} \]

### Final Answer
Thus, the spin-only magnetic moment value of \( B_2^+ \) species is:

\[ \boxed{173} \]