Question: What is a way of determining the atomic weight of an element?
About the article "Atomic number", section "Abstract".

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Definition (and closely related term).
The IUPAC definition of relative atomic mass is:An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of C. The definition deliberately specifies "An atomic weight…", as an element will have different relative atomic masses depending on the source.
For example, boron from Turkey has a lower relative atomic mass than boron from California, because of its different isotopic composition.
Nevertheless, given the cost and difficulty of isotope analysis, it is usual to use the tabulated values of standard atomic weights which are ubiquitous in chemical laboratories. 
Iodine is an essential trace element for life, the heaviest element commonly needed by living organisms, and the second-heaviest known to be used by any form of life (only tungsten, a component of a few bacterial enzymes, has a higher atomic number and atomic weight). 
 Relative atomic mass (not to be confused with relative isotopic mass) is a synonym for atomic weight, and in some circumstances may even be synonymous with "standard" atomic weight (depending on the sample, see below).
It is an average atomic mass, or the weighted mean of the atomic masses of all the atoms of a particular chemical element found in a particular sample, which is then standarized by comparison to carbon-12.
Relative atomic mass is frequently used as a synonym for the "standard" atomic weight and it is correct to do so if the relative atomic mass used is that for an element from Earth under defined conditions.
However, relative atomic mass covers more than standard atomic weights, and is a less specific term that may more broadly refer to non-terrestrial environments and highly specific terrestrial environments that deviate from Earth-average or have different certainties (number of significant figures) than do the standard atomic weights.
"Standard" atomic weight refers to the relative atomic mass or atomic weight of an element "in the local environment of the Earth's crust and atmosphere as determined by the IUPAC Commission on Atomic Weights and Isotopic Abundances."
Because these standard atomic weights are an average (mean) of relative isotopic masses for a given element from different sources (places on Earth), standard atomic weights are subject to natural variation.
An uncertainty in brackets is therefore included in sources of standard atomic weights, which often reflects natural variability in isotopic distribution for an element, rather than uncertainty in measurement.
Although there is an attempt to cover the range of variability on Earth with standard atomic weight figures, there are known cases of mineral samples which contain elements with atomic weights that are outliers from the standard atomic weight range.
Lithium represents a unique case where the natural abundances of the isotopes have in some cases been found to have been perturbed by human isotopic separation activities to the point of affecting the uncertainty in its standard atomic weight, even in samples obtained from natural sources, such as rivers.
For synthetic elements the isotope formed depends on the means of synthesis, so the concept of natural isotope abundance has no meaning.
Therefore, for synthetic elements the total nucleon count of the most stable isotope (i.e., the isotope with the longest half-life) is listed in brackets, in place of the standard atomic weight.
When the term "atomic weight" is used in chemistry, usually it is the more specific standard atomic weight that is implied.
It is standard atomic weights that are used in periodic tables and many standard references in ordinary terrestrial chemistry.   
  William Prout anonymously publishes his hypothesis that the atomic weight of every element is an integer multiple of that of hydrogen.  
Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom, which is "Z" (the atomic number).
The configuration of these electrons follows from the principles of quantum mechanics.
The number of electrons in each element's electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior.
Hence, it is the atomic number alone that determines the chemical properties of an element; and it is for this reason that an element can be defined as consisting of "any" mixture of atoms with a given atomic number.