2 Physics and MeasurementSOLUTIONS TO PROBLEMSSection 1.1Standards of Length, Mass, and TimeNo problems in this sectionSection 1.2Matter and Model-BuildingP1.1From the figure, we may see that the spacing between diagonal planes is half the distance betweendiagonally adjacent atoms on a flat plane. This diagonal distance may be obtained from thePythagorean theorem, LLLdiag=+22. Thus, since the atoms are separated by a distanceL=0 200.nm, the diagonal planes are separated by 120 14122LL+=.nm.Section 1.3Density and Atomic Mass*P1.2Modeling the Earth as a sphere, we find its volume as 43436 37101 0810363213ππr=×=×..mmej. Itsdensity is then ρ==××=×mV5 98101 08105 52102421333...kgmkgm. This value is intermediate between thetabulated densities of aluminum and iron. Typical rocks have densities around 2 000 to3 0003kg
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