The Exclusion Principle and the Periodic Table

en · official · sha256:6e55dfc73e54366136009615ffa0c0b5c38b61cb9b951e47839995423fa303fd

<definition id="fs-id1170903010005"> <term>Pauli’s exclusion principle</term> <meaning id="fs-id1170902957232">no two electrons in an atom can have the same values for all four quantum numbers <m:math><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>n</m:mi><m:mo>,</m:mo><m:mi>l</m:mi><m:mo>,</m:mo><m:mi>m</m:mi><m:mo>,</m:mo><m:msub><m:mi>m</m:mi><m:mi>s</m:mi></m:msub><m:mo stretchy="false">)</m:mo></m:mrow></m:math></meaning> </definition>

Referencing norms: TwoElectronsSharingAllFourNumbersAreForbidden, TwoSpinDownElectronsSharingAllFourNumbersAreForbidden, electron_of

en · official · sha256:0f964fd0c7c943291da5ffc4c29668deb998bcfdc2c3e99dc2e153e554c99a61

<para id="fs-id1170902772689">The structure and chemical properties of atoms are explained in part by <term id="term-00001">Pauli’s exclusion principle</term>: No two electrons in an atom can have the same values for all four quantum numbers <m:math><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>n</m:mi><m:mo>,</m:mo><m:mi>l</m:mi><m:mo>,</m:mo><m:mi>m</m:mi><m:mo>,</m:mo><m:msub><m:mi>m</m:mi><m:mi>s</m:mi></m:msub><m:mo stretchy="false">)</m:mo><m:mo>.</m:mo></m:mrow></m:math> This principle is related to two properties of electrons: All electrons are identical (“when you’ve seen one electron, you’ve seen them all”) and they have half-integral spin <m:math><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>s</m:mi><m:mo>=</m:mo><m:mn>1</m:mn><m:mtext>/</m:mtext><m:mn>2</m:mn><m:mo stretchy="false">)</m:mo><m:mo>.</m:mo></m:mrow></m:math> Sample sets of quantum numbers for the electrons in an atom are given in <link target-id="fs-id1170902930686"/>. Consistent with Pauli’s exclusion principle, no two rows of the table have the exact same set of quantum numbers.</para>

Referencing norms: PresentedConfigurationIsAdmissibleUnlessRefuted, configuration_presented

en · official · sha256:3d1a441fe1a2c701af82d3512e3158a823d82d9ce5f26337b0ac7045f10b999e

<para id="fs-id1170901705860">In the 2<emphasis effect="italics">s</emphasis> <m:math><m:mrow><m:mo stretchy="false">(</m:mo><m:mi>l</m:mi><m:mo>=</m:mo><m:mn>0</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math> subshell, the maximum number of electrons is 2. In the 2<emphasis effect="italics">p</emphasis> (<m:math><m:mrow><m:mi>l</m:mi><m:mo>=</m:mo><m:mn>1</m:mn></m:mrow></m:math>) subshell, the maximum number of electrons is 6. Therefore, the total maximum number of electrons in the <m:math><m:mrow><m:mi>n</m:mi><m:mo>=</m:mo><m:mn>2</m:mn></m:mrow></m:math> shell (including both the <m:math><m:mrow><m:mi>l</m:mi><m:mo>=</m:mo><m:mn>0</m:mn></m:mrow></m:math> and 1 subshells) is <m:math><m:mrow><m:mn>2</m:mn><m:mo>+</m:mo><m:mn>6</m:mn></m:mrow></m:math> or 8. In general, the maximum number of electrons in the <emphasis effect="italics">n</emphasis>th shell is <m:math><m:mrow><m:mn>2</m:mn><m:msup><m:mi>n</m:mi><m:mn>2</m:mn></m:msup><m:mo>.</m:mo></m:mrow></m:math></para>

Referencing norms: ShellHoldsTwiceNSquared, shell_asked

en · official · sha256:4faef466a8812017c240ad4ee0de81bfb62a5abe0cb473ecd6f4f6cb0f34739b

<para id="fs-id1170901571182">The maximum number of electrons in a subshell depends on the value of the angular momentum quantum number, <emphasis effect="italics">l</emphasis>. For a given a value <emphasis effect="italics">l</emphasis>, there are <m:math><m:mrow><m:mn>2</m:mn><m:mi>l</m:mi><m:mo>+</m:mo><m:mn>1</m:mn></m:mrow></m:math> orbital angular momentum states. However, each of these states can be filled by two electrons (spin up and down, <m:math><m:mrow><m:mo>↑</m:mo><m:mo>↓</m:mo></m:mrow></m:math>). Thus, the maximum number of electrons in a subshell is</para>

Referencing norms: SubshellHoldsTwiceTwoLPlusOne, subshell_asked