Double Magic Numbers: Not Always Guaranteed Stability

In the shell model of the nucleus, there are certain magic numbers of nucleons (protons or neutrons): 2, 8, 20, 28, 50, 82, 126 that are more tightly bound than the next higher integer. A magic number of nucleons is important because it increases the likelihood that isotopes will be stable. If the number of neutrons and protons are both  magic numbers (not necessarily the same one) we say the nucleus is doubly magic, and it is even more likely to be stable. Isotopes with doubly magic numbers include :

⁴He

¹⁶O
⁴⁰Ca, ⁴⁸Ca
⁵⁶Ni, ⁴⁸Ni
¹³²Sn
²⁰⁸Pb

None of the above isotopes are radioactive except for nickel’s pair and ¹³²Sn, which, in spite of its double magic number of 50 protons and 82 neutrons, has a half life of less than a day. So a while ago, I contacted a scientist to ask him why ¹³²Sn is radioactive.
Here is the answer from Alex Brown of the National Superconducting Cyclotron Laboratory http://www.nscl.msu.edu

Sn-132 is doubly-magic, but being doubly-magic does not guarantee stability. There are other features that can make a nucleus unstable. In this case Sn-132 is too far from the “valley of stability” – it has too many neutrons. The neutrons in Sn-132 beta decay and turn into protons eventually leading to the most stable mass 132 nucleus Xe-132.
The “magic number” of 50 protons for Sn does show up by the fact that Sn has more stable isotopes than any other element – they are: Sn-112, Sn-114, Sn-115, Sn-116, Sn-117, Sn-118, Sn-119, Sn-120, Sn-122 and Sn-124. There are other nuclei that we predict to be doubly-magic that are unstable, such as Sn-100 and Ni-78.
At our National Superconducting Cyclotron Laboratory are are trying to produce these nuclei and study their properties.

 A little side note: A proton consists of  uud, where u = upquark, d= down quark. For a neutron the recipe is reversed: ddu. The total number of upquarks is therefore equal to mass number plus atomic number(which equals number of protons). This is because mass number, M = p+n and n = M-p.  Since there are two upquarks per proton and only 1 per neutron, the total number of upquarks is M-p + 2p = M+p. For dowquarks the sum is 2(M-p) + p = 2M -p.

Modified Palm Oil In Cheap Chocolate

Most readers are well-acquainted with trans fats and the classic Nurse’s Study published in the New England Journal of Medicine. Most of the ensuing legislation that either banned or limited the content of trans fats in groceries was rooted in one of the  conclusions from that study:

the replacement of 2 percent of energy from trans fat with energy from unhydrogenated, unsaturated fats would reduce risk of coronary heart disease by 53 percent (95 percent confidence interval, 34 to 67; P<0.001)

It’s also common knowledge that a portion of the food industry responded to the new limitations by turning to palm oil as a substitute. So-called palm oil is actually a solid at sub-tropical temperatures because it melts at 33 to 39 ^oC. The reason for the melting point range is that palm oil like most triglycerides in food is not a single compound but a mixture of similar ones. But to create that trans-fat like texture the melting point is too high. So what’s the solution?

First a quick review of triglyceride chemistry. A triglyceride is basically an ester, formed in nature by the reaction of  fatty acids and glycerol. 

Here is a general formula for a triglyceride, whose properties will vary depending on the alkyl groups (R₁, R₂ and R₃: highlighted in red). The glycerol skeleton is highlighted in blue.

The R₁, R₂ and R₃ groups are basically fatty acids minus the -CO₂ group that’s already represented in the general structural formula. Here are three examples of fatty acids.

Cocoa butter is a triglyceride obtained from the cocoa bean, and it is used to make chocolate. When mixed with the right ingredients, it’s delicious. In addition, the fairly constant combination of fatty acids found in the beta form give this triglyceride another desirable property: a sharp melting point of 35 to 37^oC, which coincides with the average range of human mouth temperatures. But cocoa butter is expensive, so in the past some of it was substituted with partially hydrogenated oils. Once anti-trans fat laws were passed, manufacturers of inexpensive chocolate could not simply use palm oil, whose melting point is not sharp enough. So what they did instead is rely on the interesterification of triglycerides, one of several methods of “modifying an oil”. Eighty percent of cocoa butter triglycerides have palmitic and stearic acids in the R₁  and R₃ positions with oleic acid in the R₂ slot. To create an impostor molecule from palm oil, a stearic acid residue is introduced at the R₁  and R₃ positions, where it’s normally absent.
There are different ways of interesterifying. The superior method relies on enzymes because it leaves the R₂ position unchanged. The catalyst that creates a greater hodge-podge of products is sodium methoxide. In either case, we don’t exactly have the equivalent of a “Nurse’s Study” to investigate the health impact of these molecules that are being included in foods.

Look for modified palm oil in the average candy bar and especially in cheap Easter chocolate, where it is the second most common ingredient after sugar. It is also found in albeit smaller quantities (3 to 5%) in several versions of trans fat -free margarine. Another common recipe for chocolate products such as Nutella also includes sugar at its main ingredient, followed by palm oil instead of modified palm oil. The former is one of the few vegetable oils high in saturated fat due its main ingredient, palmitate, an ester of palmitic acid, C₁₆H₃₂O₂.

REFERENCES

http://palmoil.com/useful_info/dd          Information about palm oil from the industry
http://www.nejm.org/doi/full/10.1056/NEJM199711203372102   The Nurse’s Study
http://www.lsbu.ac.uk/biology/enztech/interester.html  More details on interesterification
http://www.canada.com/topics/news/story.html?id=fd113bdf-6686-496a-8161-06a85546a1b8A General article on modified fats