Question

(a) What is the minimum value of 1 for a subshell that has 11 electrons in it?

(b) If this subshell is in the n = 5shell, what is the spectroscopic notation for this atom?

Short answer

(a) The value ofl is obtained as :3

(b) The spectroscopic notation for this atom is obtained as: 5f¹¹ .

Step-by-step solution

Determine the formula:

Consider the formula for the number of electrons is:

\({{\bf{n}}_{\bf{e}}}{\bf{ = 2}}\left( {{\bf{2l + 1}}} \right)\)

Here,\(l\)is the angular momentum.

Rewrite the expression in terms of the angular momentum as:

\({\bf{l = }}\frac{{\frac{{{{\bf{n}}_{\bf{e}}}}}{{\bf{2}}}{\bf{ - 1}}}}{{\bf{2}}}\)

Evaluate the number of electrons

(a)

Substitute the values and solve as:

\(\begin{array}{c}l = \frac{{\frac{{{n_e}}}{2} - 1}}{2}\\ = \frac{{\frac{{11}}{2} - 1}}{2}\\ = 2.25\\ \approx 3\end{array}\)

Therefore, the minimum value ofl is: 3.

Evaluate the spectroscopic notation

(b)

As, the it is known that the value as: n = 5.

The subshell is of the value f.

So, the spectroscopic notation is: 5f¹¹.

Therefore, the spectroscopic notation for this atom is: 5f¹¹ .