Question regarding atomic weight percentage, and concentration

[sandy.bridge]

One of the examples I was looking at had to do with diffusion of hydrogen in a Pb sheet. There is a constant concentration gradient applied, so the hydrogen is constantly diffusing. We are able to determine the concentration of the Pd matrix. We further know the atomic weight percentages of the hydrogen at either end of the concentration gradients. Let's say 1 at. % at one end, and 0.2 at. % at the other. To determine the concentration of hydrogen, he merely multiplied the concentration of Pd by the percentages (0.01, 0.002). Is this correct? I though you would have to multiply TOTAL concentration of both hydrogen and Pd atoms?

The atomic percentage of atom A is number of A atoms/(number of A atoms + number of B atoms)??

 

[Borek]

Concentration of what in what and where? There is a concentration gradient, so I suppose you are talking about concentration of hydrogen in "surface layer" (whatever it exactly means)?

Perhaps what you are looking for is this: if B>>A then A/(A+B)≈A/B.

 

[sandy.bridge]

That is exactly what I was looking for, and I figured it was the case. Is there a rule of thumb as to what constitutes B>>A?

 

[Borek]

It depends on the application. Sometimes 5% accuracy is enough, sometimes not. But if B is less than 1% of A I would have no problems with using it.

You can always estimate if it makes sense to use this approximation remembering that

$$\frac a {a+b} = \frac a b - \frac {a^2} {b^2} + \frac {a^3} {b^3} - \frac {a^4} {b^4}\dots$$

(for a close to zero). Note that

$$\frac {0.01} {1+0.01} = 0.0099(0099)$$

and

$$\frac {0.01} {1} - \frac {0.01^2}{1^2} = 0.0099$$

so given accuracy of most numbers we are dealing with, we are already good after the first two terms.