<Dl> <Dd> h = c α 2 A r (e) M u 2 R ∞ N A . (\ displaystyle h = (\ frac (c \ alpha ^ (2) A_ (\ rm (r)) ((\ rm (e))) M_ (\ rm (u))) (2R_ (\ infty) N_ (\ rm (A)))).) </Dd> </Dl> <Dd> h = c α 2 A r (e) M u 2 R ∞ N A . (\ displaystyle h = (\ frac (c \ alpha ^ (2) A_ (\ rm (r)) ((\ rm (e))) M_ (\ rm (u))) (2R_ (\ infty) N_ (\ rm (A)))).) </Dd> <P> The measurements use highly polished spheres of silicon with a mass of one kilogram . Spheres are used to simplify the measurement of the size (and hence the density) and to minimize the effect of the oxide coating that inevitably forms on the surface . The first measurements used spheres of silicon with natural isotopic composition, and had a relative uncertainty of 3.1 × 10 . These first results were also inconsistent with values of the Planck constant derived from watt balance measurements, although the source of the discrepancy is now believed to be known . </P> <P> The main residual uncertainty in the early measurements was in the measurement of the isotopic composition of the silicon to calculate the atomic weight, so in 2007 a 4.8 kg single crystal of isotopically - enriched silicon (99.94% Si) was grown, and two one - kilogram spheres cut from it . Diameter measurements on the spheres are repeatable to within 0.3 nm, and the uncertainty in the mass is 3 μg . Full results from these determinations were expected in late 2010 . Their paper, published in January 2011, summarized the result of the International Avogadro Coordination and presented a measurement of the Avogadro constant to be 7023602214078000000 ♠ 6.022 140 78 (18) × 10 mol . </P>

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