Say we got an alloy made of 90% Au and 10%Cu. The atomic mass of gold is A A u = 197 g / m o l eand of copper A C u = 63.5 g / m o l eThe specific resistivity of gold is ρ = 22.8 n Ω mand the Nordheim coefficient is C = 450 n Ω mThen by the Nordheim rule we have that the resistivity of this alloy is given as ρ = ρ A u + C X ( 1 − X )where X=0.1, and represents the percentage of Copper in the alloy. Using the above I got that ρ = 63.3 n Ω m, but data shows that the actual resistivity is ρ = 108 n Ω m. What about X? Is it the percentage of atoms in the alloy, or is it the percentage of mass in the alloy?

Question

Say we got an alloy made of   90% Au and 10%Cu. The atomic mass of gold is      A          A      u        =  197  g      /    m  o  l  eand of copper      A          C      u        =  63.5  g      /    m  o  l  eThe specific resistivity of gold is  ρ  =  22.8  n  Ω  mand the Nordheim coefficient is  C  =  450  n  Ω  mThen by the Nordheim rule we have that the resistivity of this alloy is given as  ρ  =      ρ          A      u        +  C  X  (  1  −  X  )where X=0.1, and represents the percentage of Copper in the alloy. Using the above I got that  ρ  =  63.3  n  Ω  m, but data shows that the actual resistivity is   ρ  =  108  n  Ω  m. What about X? Is it the percentage of atoms in the alloy, or is it the percentage of mass in the alloy?

kazneni3tr2b · Accepted Answer

The resistivity is dependent on the number of atoms and so you must find the ratio of copper atoms to the total number of atoms to find X and hence the resistivity of the alloy.If you do this correctly you should find that the value you have calculated is in agreement with the book value.The molar fraction of copper (fraction of copper atoms to the copper and gold atoms) is given by  X  =                    (                              10            63.5                          )                    (                              10            63.5                          +                              90            197                          )              =            394      1537      This comes from the idea that 10 g of copper is             10      63.2       moles of copper which is             10      63.2        ×      N          A       atoms of copper where       N          A       is Avagadro&#039;s constant.  ρ  =  22.8  +  450  ×            394      1537            (    1    −                  394        1537              )    =  108.6

Say we got an alloy made of 90 % Au and 10%Cu. The atomic mass of gold is A <m

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