That's a 5% difference. Should easily be able to detect by specific gravity test.
Not so, unfortunately. Atomic weight is not the same as density. Atomic weight is the weight of one mole , or 6.02 x 10**23 atoms, of a substance. Atomic weight says nothing about the volume occupied by one mole of a substance so you can't just weigh two bars of equal size and expect a 5% difference in weight if one is gold and the other tungsten.
—yep—considering that the concept is three thousand years or so old, you’d think some of these financial geniuses would know about it-—