Q: I have recently discovered the existence of the following extreme SI prefixes and their symbols: zepto (z) (10鈭�21), yocto (y) (10鈭�24), zetta (Z) (1021) and yotta (Y) (1024). Can anyone suggest some uses to which these extreme values could be put? (As an example, perhaps the radius of the known Universe is about one yottametre.)
A: The suggestion that the radius of the known Universe might be one yottametre is a couple of orders of magnitude too low. The distance of the most remote object yet observed (the quasar PC1247+ 3406), estimated from its red shift, is about 125 yottametres. Whether this is more comprehensible than saying it is 1.25 脳 1023 kilometres or 13.2 billion light years away, is debatable. The largest known galaxy, at the centre of the Abell 2029 cluster in Virgo, has a diameter of around 53 zettametres.
At the other extreme, the atomic mass unit (mu) offers a use for the yocto prefix (10鈭�24). Normally quoted as 1.66 脳 10鈭�27 kilograms, this unit can be expressed as 1.66 yoctograms.
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Do these extreme prefixes serve any purpose? To perform calculations or simply make comparisons, we must use the basic SI units with the appropriate powers of 10. It must be said, though, that the above examples do look neater in print using the micro/macro units.
A: New SI prefixes are welcome as they allow powers of 10 to all but vanish from our text. Constants, in particular, are now much easier to write and remember. Also, several big-number units can be discarded and replaced with the new SI equivalent. For example, we no longer need to think in electronvolts for one eV is 160 zeptojoules (zJ); one Earth mass is now simply 5977 yottagrams (Yg), and the planets can be measured in Yg and moons in zettagrams (Zg). One molecule is now simply 1.661 yoctomoles.
A: The SI prefixes above are not the only extreme ones. Others such as xenno (x) (10鈭�27) and xenna (X) (1027), or vendeko (v) (10鈭�33) and vendeka (V) (10鈭�33) exist, and can help simplify the expression of extreme numbers. Below are some examples of situations in which SI prefixes for extremes could be quite useful.
Many galaxies are more than 1 billion light years distant, about 1025 metres. The Andromeda galaxy is about 2 脳 1022 metres or 20 zettametres (Zm) distant, and the Magellanic clouds are about 1.5 脳 1021 metres distant, or 1.5 Zm.
Avogadro鈥檚 number, the number of molecules in a mole of substance, is 6.02252 脳 1023. Thus one molecule of a substance dissolved in 1 litre of water has a concentration of 1.7 脳 10鈭�24mol/1 or 1.7 yoctomol/l. Homeopaths might like to have prefixes to indicate even lower concentrations, since they habitually dilute solutions of drugs until they have excluded active molecules altogether. Boltzmann鈥檚 entropy constant (the gas constant divided by Avogadro鈥檚 number) is 1.4 脳 10鈭�23 joules per kelvin or 14 yoctojoules per kelvin.
The elementary charge is 1.6 脳 10鈭�19 coulombs (160 zeptocoloumbs) and the mass of a proton is 1.7 yoctograms.
A magneton is a unit of magnetic moment. The Bohr magneton (from Bohr鈥檚 theory of the atom) is 9.27 脳 10鈭�24 joules per tesla and the nuclear magneton is 5.05 脳 10鈭�27 joules per tesla. The magnetic moment of an electron is 9.3 脳 10鈭�24 joules per tesla and a proton 1.4 脳 10鈭�26 joules per tesla.
A: There is a characteristic time scale for nuclear phenomena: the amount of time, T, it takes for light to traverse a distance equal to the radius of a proton. Take, for simplicity鈥檚 sake, the proton radius to be 1 femtometre (10鈭�15), then the characteristic nuclear time scale is T = 0.3 脳 10鈭�21 seconds, or 0.3 zeptoseconds. This corresponds to a frequency (1/T) = 3 脳 10 hertz, or 3 zettahertz. An electromagnetic quantum with frequency of 3 zettahertz carries energy equal to approximately 2 脳 10鈭�12 joules (or, in the more familiar nuclear physics units, 2 megaelectronvolts) which is a typical value for a gamma ray emitted from an excited atomic nucleus.
A: Zetta (1021) could be used to give the number of letters in all the words in all the books in all the libraries in the world. But as extreme numbers go, a zetta isn鈥檛 really that large.
Ancient Indian writings contain descriptions of large stretches of time. One such is this: 鈥淚magine a stone, a cubic mile in size, a million times harder than diamond. Every million years a very holy man visits it to give the lightest possible touch. The stone is in the end worn away. How many years would this take?鈥� The answer is about 1035 years.
Using 1051 (a little larger than a yotta squared) would let you compare the size of the smallest particle in the Universe with the size of the entire observable Universe. And 1051 is also the number of grains of sand in the Universe as calculated by Archimedes two thousand years ago. According to a calculation by Arthur Eddington earlier this century, there are about 1080 subatomic particles in the Universe. This is almost, but not quite, a googol 鈥� a googol being 10100 or approximately a yotta squared, squared.
A googol is a 1 followed by 100 zeros. A 1 followed by 65 000 zeros is about the size of the largest prime number yet discovered. I鈥檓 sure you鈥檝e heard the phrase that the likelihood of something is 鈥渁bout the same as a chimpanzee typing out the complete works of Shakespeare鈥�. The probability of this happening is one chance in a number which is 100 000 digits long.
There are at least two larger named numbers than these. One is called a googolplex, which is 10 to the power of a googol. A googolplex is in fact the same size as the number of possible games of chess. But the largest number ever needed to solve a genuine problem (in pure mathematics) is a number called Skewes鈥� number, which appears in a branch of maths called number theory. This number is stated as 10鈫�(10鈫�(10鈫�34)) [10鈫�10 means the same as 1010] and is almost impossibly large to describe. The best I can do is to say it is not quite as large as 10 to the power of a googolplex.
There is a named number which is larger than Skewes鈥� number. This is Graham鈥檚 number, used in a part of combinatorics called Ramsey theory, and it is so large that a new number notation system had to be introduced to define it. Apparently, if all the material in the Universe were turned into writing materials it would not be enough to write the number down 鈥� Ed.
A: There鈥檚 nothing extreme about yotta values. I frequently offer my guests wine in yottameasures. It sounds impressive but, assuming 15 per cent alcohol, 1024 wine molecules occupy approximately 33 millilitres 鈥� about half a stingy glass.