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Chapter 8: Problem 58

(a) What is the minimum value of \(l\) for a subshell that contains 11 electrons? (b) If this subshell is in the \(n=5\) shell, what is the spectroscopic notation for this atom?

Short Answer

Expert verified
(a) The minimum value of \(l\) for a subshell containing 11 electrons is \(l = 3\). (b) The spectroscopic notation for this atom in the \(n=5\) shell is 5f.

Step by step solution

01

Determining the total number of electrons in the subshell

To find the minimum value of l for a subshell containing 11 electrons, let's first determine the total number of electrons that can fit in each subshell. This capacity is determined by the formula: \[Capacity = 2(2l + 1)\] Where l is the orbital angular momentum.
02

Calculating l values and determining the minimum l

We will now find out the subshell with the lowest possible l value that can accommodate at least 11 electrons. For this, we calculate the electron capacity for increasing l values. Starting with l = 0: \[Capacity = 2(2(0) + 1) = 2\] Since the capacity is less than 11, we increase l to 1: \[Capacity = 2(2(1) + 1) = 6\] Still less than 11, so l is increased to 2: \[Capacity = 2(2(2) + 1) = 10\] Not yet 11, so let's try with l=3: \[Capacity = 2(2(3) + 1) = 14\] Now, the electron holding capacity is 14, which is greater than 11. So, the minimum value of l for a subshell containing 11 electrons is 3. (a) Minimum value of l: l = 3
03

Spectroscopic notation for the atom

To find the spectroscopic notation of the atom, we use the following format: \[\mathrm{Principal\:quantum\:number\:}\mathrm{(n)}\mathrm{\:-\:}\mathrm{Orbital\:Symbol}\] Where the Orbital Symbol is derived from the value of l as follows: - l = 0 corresponds to s - l = 1 corresponds to p - l = 2 corresponds to d - l = 3 corresponds to f Since this subshell is in the n=5 shell, and l=3, it is in the f subshell. So, the spectroscopic notation for this atom is: (b) 5f

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Most popular questions from this chapter

Show that the maximum number of electron states in the \(n\) th shell of an atom is \(2 n^{2}\).

Compare the electron configurations of the elements in the same column of the periodic table.

List all the possible values of \(s\) and \(m_{s}\) for an electron. Are there particles for which these values are different?

(a) If one subshell of an atom has nine 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?

What is the total number of states with orbital angular momentum \(l=0\) ? (Ignore electron spin.)
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