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Neutron–proton ratio
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The neutron–proton ratio (N/Z ratio or nuclear ratio) of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than strong nuclear force attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions.
For each element with atomic number Z small enough to occupy only the first three nuclear shells, that is up to that of calcium (Z = 20), there exists a stable isotope with N/Z ratio of one, with the exception of beryllium (N/Z = 1.25) and every element with odd atomic number between 9 and 19 inclusive (N = Z+1). Hydrogen-1 (N/Z ratio = 0) and helium-3 (N/Z ratio = 0.5) are the only stable isotopes with neutron–proton ratio under one. Uranium-238 and plutonium-244 have the highest N/Z ratios of any primordial nuclide at 1.587 and 1.596, respectively, while lead-208 has the highest N/Z ratio of any known stable isotope at 1.537. Radioactive decay generally proceeds so as to change the N/Z ratio to increase stability. If the N/Z ratio is greater than 1, alpha decay increases the N/Z ratio, and hence provides a common pathway towards stability for decays involving large nuclei with too few neutrons. Positron emission and electron capture also increase the ratio, while beta decay will decrease the ratio.
Nuclear waste exists mainly because nuclear fuel has a higher stable N/Z ratio than the parts into which it is fissioned.
Semi-empirical description[edit]
For stable nuclei, the neutron-proton ratio is such that the bonding energy is at a local minimum or close to a minimum.
From the liquid drop model, this bonding energy is approximated by empirical Bethe–Weizsäcker formula
E B = a V A − a S A 2 / 3 − a C Z 2 A 1 / 3 − a A ( A − 2 Z ) 2 A ± δ ( A , Z ) . {\displaystyle E_{B}=a_{V}A-a_{S}A^{2/3}-a_{C}{\frac {Z^{2}}{A^{1/3}}}-a_{A}{\frac {(A-2Z)^{2}}{A}}\pm \delta (A,Z).}
Given a value of A {\displaystyle A} and ignoring the contributions of nucleon spin pairing (i.e. ignoring the ± δ ( A , Z ) {\displaystyle \pm \delta (A,Z)} term), the binding energy is a quadratic expression in Z {\displaystyle Z} that is minimized when the neutron-proton ratio is N / Z ≈ 1 + a C 2 a A A 2 / 3 {\displaystyle N/Z\approx 1+{\frac {a_{C}}{2a_{A}}}A^{2/3}} .
Isotope half-lives. Note that the plot for stable isotopes diverges from the line Z = N as the element number Z becomes larger
See also[edit]
Isotope#Variation in properties between isotopes
Nuclear fission
Nuclear drip line

This nuclear physics or atomic physics–related article is a stub. You can help Wikipedia by expanding it.
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Swiss chalet style
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Schweizerhaus in Klein Glienicke near Berlin, designed by Ferdinand von Arnim, 1867
Swiss chalet style (German: Schweizerstil, Norwegian: Sveitserstil) is an architectural style of Late Historicism, originally inspired by rural chalets in Switzerland and the Alpine (mountainous) regions of Central Europe. The style refers to traditional building designs characterised by widely projecting roofs and facades richly decorated with wooden balconies and carved ornaments. It spread over Germany, Austria-Hungary and Scandinavia during the Belle Époque era.
Contents
[hide]
1 History
2 Characteristics
3 See also
4 References
History[edit]
Villa Fridheim in Krødsherad, Norway
Swiss chalet style originated in the Romantic era of the late-18th/early-19th century, when the ideas of the English landscape garden inspired parks and residences in Germany, such as the Dessau-Wörlitz Garden Realm. It became highly appreciated on the continent by noble landowners who were impressed by the "simple life" of people living in the mountains.
The chalet style soon spread over the German Mittelgebirge landscapes such as the Harz mountains or the Dresden area and the adjacent North Bohemian region. As a "modern" building style, it also influenced the resort architecture along the Baltic seaside, like in Binz or Heringsdorf. Around 1900, design elements were used in the construction of numerous bourgeois family homes as well as by notable architects like Heinrich von Ferstel to build larger mansions and hotels.
The style was further popularized by the first waves of tourism of rich people from the North and West of Europe and became popular in other parts of Europe and North America, notably in the architecture of Norway, Iceland and the Netherlands and in the country house architecture of Sweden and Cincinnati (Ohio, USA), in the late 19th and early 20th century. English examples of the chalet style include the Boathouse at Belton House, Lincolnshire, by Anthony Salvin and the Swiss Cottage at Osbourne House, on the Isle of Wight, constructed for Queen Victoria's children.
Characteristics[edit]
The style is characterized by:
Gabled roofs with wide eaves
Exposed construction beams, including large brackets
Decorative carving and mouldings
Balconies
Large windows
Weatherboarding, usually painted, often in bright colors
Villa in Erlangen
Villa Eschebach in Dresden
Kviknes Hotel in Balestrand, Norway, planned by Franz Wilhelm Schiertz in 1894
Hotel Rooding in Valkenburg (1892), designed by Pierre Cuypers
See also[edit]
Victorian architecture
Carpenter Gothic
Norvell House
Timeline of architectural styles
References[edit]
Cincinnati Swiss Chalet houses
Norwegian description of Swiss Chalet style
DESIGN I. Swiss Chalet, P. F. Robinson, architect, 1827. no online picture
Wikimedia Commons has media related to Swiss chalet style architecture.
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