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Grimm–Sommerfeld rule

Grimm–Sommerfeld rule is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Grimm–Sommerfeld rule rather than just read about it. In short: In chemistry, the Grimm–Sommerfeld rule predicts that binary compounds with covalent character that have an average of 4 electrons per atom will have structures where both atoms are tetrahedrally coordinated (e.g. have the wurtzite structure). Examples are silicon carbide, the III-V semiconductors indium phosphide and gallium arsenide, the II-VI semiconductors, cadmium sulfide, cadmium selenide.

Key takeaways

  • Grimm–Sommerfeld rule belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Grimm–Sommerfeld rule to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Grimm–Sommerfeld rule from memory before moving on to harder problems.

Reference excerpt

In chemistry, the Grimm–Sommerfeld rule predicts that binary compounds with covalent character that have an average of 4 electrons per atom will have structures where both atoms are tetrahedrally coordinated (e.g. have the wurtzite structure). Examples are silicon carbide, the III-V semiconductors indium phosphide and gallium arsenide, the II-VI semiconductors, cadmium sulfide, cadmium selenide. Gorynova expanded the scope of the rules to include ternary compounds where the average number of valence electrons per atom was four. Examples of this are the I-IV2-V3 CuGe2P3 compound which has a zincblende structure. Compounds or phases that obey the Grimm–Sommerfeld rule are termed Grimm–Sommerfeld compounds or phases. The rule has also been extended to predict bond lengths in Grimm–Sommerfeld compounds. When the sum of the atomic numbers is the same the bond lengths are the same. An example is the series of bond lengths ranging from 244.7 pm to 246 pm. for the Ge–Ge bond in elemental germanium, the Ga–As bond in gallium arsenide, the Zn–Se bond in zinc selenide and the Cu–Br bond in copper(I) bromide.

References

Worked examples

Example 1 — a first encounter with Grimm–Sommerfeld rule

Start with the simplest possible case. Write down what Grimm–Sommerfeld rule claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Grimm–Sommerfeld rule before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Grimm–Sommerfeld rule ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Grimm–Sommerfeld rule

In research
Grimm–Sommerfeld rule appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Grimm–Sommerfeld rule in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Grimm–Sommerfeld rule is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum chemistry, Quantum chemistry stubs, so understanding it makes those chapters shorter.
In everyday life
Look for Grimm–Sommerfeld rule outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Grimm–Sommerfeld rule in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Grimm–Sommerfeld rule means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Grimm–Sommerfeld rule out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Grimm–Sommerfeld rule in simple terms?

In chemistry, the Grimm–Sommerfeld rule predicts that binary compounds with covalent character that have an average of 4 electrons per atom will have structures where both atoms are tetrahedrally coordinated (e.g. have the wurtzite structure). Examples are silicon carbide, the III-V semiconductors…

Why does Grimm–Sommerfeld rule matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Grimm–Sommerfeld rule?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Grimm–Sommerfeld rule.

Tags

  • Quantum chemistry
  • Quantum chemistry stubs

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