If `Z_("eff")` of Mg is 2.85, then what will be the value of y for magnesium, where `y = ((sigma + 0.85))/(2)` ?

Answer

To solve the problem, we need to find the value of \( y \) for magnesium given that the effective nuclear charge \( Z_{\text{eff}} \) is 2.85. The relationship provided is:

\[ y = \frac{(\sigma + 0.85)}{2} \]

where \( \sigma \) is the screening constant.

### Step 1: Identify the atomic number \( Z \) of magnesium
The atomic number \( Z \) of magnesium (Mg) is 12.

### Step 2: Calculate the screening constant \( \sigma \)
Using the formula for effective nuclear charge:

\[ Z_{\text{eff}} = Z - \sigma \]

We can rearrange this to find \( \sigma \):

\[ \sigma = Z - Z_{\text{eff}} \]

Substituting the known values:

\[ \sigma = 12 - 2.85 \]

Calculating this gives:

\[ \sigma = 9.15 \]

### Step 3: Substitute \( \sigma \) into the equation for \( y \)
Now that we have \( \sigma \), we can substitute it into the equation for \( y \):

\[ y = \frac{(9.15 + 0.85)}{2} \]

Calculating the numerator:

\[ 9.15 + 0.85 = 10 \]

Now, substituting this back into the equation for \( y \):

\[ y = \frac{10}{2} \]

### Step 4: Calculate the final value of \( y \)
Now we can calculate \( y \):

\[ y = 5 \]

Thus, the value of \( y \) for magnesium is:

\[ \boxed{5} \]