Wednesday, May 11, 2016

Copper Coins And Silver Coins

The ratio,

\(\cfrac{A_v}{A_D}=\cfrac{6.02214e26}{9.029022e26}=0.66698\)

\(\cfrac{A_D}{A_v}=1.49930\approx \cfrac{3}{2}\) or

The new number is approximately 1.5 times Avogadro's constant.

And compare these two numbers with the number stated in pound,

\(N_A = 2.73159734e26\) (lb-mol)−1

\(\cfrac{A_v}{N_A}=2.204622\) --- (*)

\(\cfrac{A_D}{N_A}=3.305400\approx\pi\)

If the definition of the pound unit included the constant \(\pi\), and

\(\cfrac{A_D}{N_A}*\cfrac{2}{3}=2.203600\approx\cfrac{A_v}{N_A}\)

from equation (*),  then we have to look carefully at the factor,

\(Err_{chg}=\cfrac{3}{2}\)

Short changed by a factor of \(\cfrac{3}{2}\) .