The number of nuclei in 1 gram of copper (Cu)

[lonewolf219]

$^{62}Cu$ is 61.932586 amu. I would like to know how many exposed nuclei are in 1.0 gram of $^{62}Cu$. I have two calculations below, hopefully one of them is correct...

Method 1.

1.0 gram $^{62}Cu$ x $\frac{1 kg}{1000 g}$ x $\frac{1 amu}{1.660566 x 10^{-27}kg}$ x $\frac{1 mole ^{62}Cu}{61.932586 amu}$ x $\frac{6.022 x 10^{23} nuclei}{1 mole ^{62}Cu}$ = 5.8555 x 10$^{45}$ $^{62} Cu$ nuclei

Method 2.

1.0 gram $^{62}$Cu x $\frac{1 mole ^{62}Cu}{61.932586 grams}$ x $\frac{6.022 x 10^{23} nuclei}{1 mole ^{62}Cu}$ = 9.723 x 10$^{21}$ $^{62}Cu$ nuclei

 

[UltrafastPED]

As an approximation you can consider one gram of matter to contain Avogadro's number worth of nucleons; since Cu-62 has 62 nucleons, the number of nuclei is Av./62 = 9.713e21.

So your method 2 is correct. Can you see what went wrong in the first method?

 

[jtbell]

In Method 1 the conversion factor 1 mole ⁶²Cu = 61.932586 amu is incorrect. In method 2 you have the correct conversion factor, 1 mole ⁶²Cu = 61.932586 g.

61.932586 amu is the mass of one atom of ⁶²Cu.

[UltrafastPED slipped in before I finished typing!]

 

[lonewolf219]

jtbell, thanks! I don't think I could have arrived at that conclusion on my own...

 

[lonewolf219]

UltraFastPED, thanks as well for your quick response... appreciate the help, as well as the rule of thumb you mentioned