science

Mattauch isobar rule

Mattauch isobar rule is a science 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 Mattauch isobar rule rather than just read about it. In short: The Mattauch isobar rule, formulated by Josef Mattauch in 1934, states that if two adjacent elements on the periodic table have isotopes of the same mass number, one of the isotopes must be radioactive. Two nuclides that have the same mass number (isobars) can both be stable only if their atomic numbers differ by more than one.

Key takeaways

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

Reference excerpt

The Mattauch isobar rule, formulated by Josef Mattauch in 1934, states that if two adjacent elements on the periodic table have isotopes of the same mass number, one of the isotopes must be radioactive. Two nuclides that have the same mass number (isobars) can both be stable only if their atomic numbers differ by more than one. In fact, for currently observationally stable nuclides, the difference can only be 2 or 4, and in theory, two nuclides that have the same mass number cannot be both stable (at least to beta decay or double beta decay), but many such nuclides which are theoretically unstable to double beta decay have not been observed to decay, e.g. 134Xe. However, this rule cannot make predictions on the half-lives of these radioisotopes.

Technetium and promethium

A consequence of this rule is that neither technetium nor promethium have any stable isotopes, as each of the neighboring elements on the periodic table (molybdenum and ruthenium, and neodymium and samarium, respectively) have a beta-stable isotope for each mass number for the range in which the isotopes of the unstable elements usually would be stable to beta decay. Samarium-147 is not a counterexample; although it is unstable to alpha decay, it is stable to beta decay. These ranges can be calculated using the liquid drop model (for example the stability of technetium isotopes), in which the isobar with the lowest mass excess or greatest binding energy is shown to be stable to beta decay because energy conservation forbids a spontaneous transition to a less stable state. Thus no stable nuclides have proton number 43 or 61, and by the same reasoning no stable nuclides have neutron number 19, 21, 35, 39, 45, 61, 71, 89, 115, or 123.

Exceptions The only known exceptions to the Mattauch isobar rule are the cases of antimony-123 and tellurium-123 and of hafnium-180 and tantalum-180m, where both nuclei are observationally stable. It is predicted that 123Te should undergo electron capture to form 123Sb, but this decay has not yet been observed; 180mTa should be able to undergo isomeric transition to 180Ta, beta decay to 180W, electron capture to 180Hf, or alpha decay to 176Lu, but none of these decay modes have been observed. In addition, beta decay has been seen for neither curium-247 nor berkelium-247, though it is expected that the former should decay into the latter. Both nuclides are alpha-unstable. As mentioned above, the Mattauch isobar rule cannot make predictions as to the half-lives of the beta-unstable isotopes. Hence there are a few cases where isobars of adjacent elements both occur primordially, as the half-life of the unstable isobar is over a billion years. This occurs for the following mass numbers:

40 (40Ar and 40Ca stable; 40K unstable) 50 (50Ti and 50Cr stable; 50V unstable) 87 (87Sr stable; 87Rb unstable) 113 (113In stable; 113Cd unstable) 115 (115Sn stable; 115In unstable) 138 (138Ba and 138Ce stable; 138La unstable) 176 (176Yb and 176Hf stable; 176Lu unstable) 187 (187Os stable; 187Re unstable)

Worked examples

Example 1 — a first encounter with Mattauch isobar rule

Start with the simplest possible case. Write down what Mattauch isobar rule claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Mattauch isobar 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 Mattauch isobar 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 Mattauch isobar rule

In research: Mattauch isobar rule appears in science 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 Mattauch isobar 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: Mattauch isobar rule is common in secondary-school and first-year university syllabi. It links to neighbouring topics Isotopes, Radioactivity, so understanding it makes those chapters shorter.
In everyday life: Look for Mattauch isobar 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 Mattauch isobar rule in 20 minutes

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

Frequently asked questions

What is Mattauch isobar rule in simple terms?

Why does Mattauch isobar rule matter?

Because it connects several science 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 Mattauch isobar 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 Mattauch isobar rule.