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Chapter 30: Q46PE (page 1113)

(a) If one subshell of an atom has 9 electrons in it, what is the minimum value of l ?

(b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?

Short Answer

Expert verified

(a) The minimum value of l for a subshell that has 9 electrons is 2.

(b) The spectroscopic notation is \(3{d^9}\).

Step by step solution

01

Determine the formulas:

Consider the formula for the number of electrons is:

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

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

02

Determine the minimum value of l if one subshell of an atom has 9 electrons in it.

a)

Given that one subshell of an atom has 9 electrons in it

Case 1: For\(l = 1\)

Solve as:

\(\begin{array}{c}n = 2\left( {2\left( 1 \right) + 1} \right)\\n = 6\end{array}\)

Case 2: For\(l = 2\)

Solve as:

\(\begin{array}{c}n = 2\left( {2\left( 2 \right) + 1} \right)\\n = 10\end{array}\)

Also,\(l\)must be a whole number.

So\(,l \ge 2\)

Hence, the minimum value of l for a subshell that has 9 electrons is 2.

03

To determine the spectroscopic notation for this atom, if this subshell is part of the n=3 shell.

b)

Given for\(n = 3,\;l = 2\)for 9 electron in the subshell

Spectroscopic notation is given as follows:

\(3{d^9}\)

Hence, the spectroscopic notation is \(3{d^9}\).

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