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what is the atomic mass of the most common isotope of silver as indicated by the periodic table?

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3 Answers

The periodic table is not useful for predicting the most stable isotope of any element.  You can make a decent guess, but it's likely you'd be wrong much of the time.  The periodic table was not constructed for nuclear chemistry; it's best to look at the chart of the nuclides (aka, table of isotopes) to answer this question.
 
The masses on the periodic table are weighted averages for all of the stable isotopes of each element.  (For the elements that have no stable isotopes, it's the most common radioactive isotope.)  It may seem rather strange that the atomic masses of each stable isotope are not integers either.  Only carbon-12 has an integer for its atomic mass; it's defined that way.  The other elements are all compared to carbon-12.  The reason for this has to do with the non-integer masses of protons and neutrons, and the mass lost when the protons and neutrons bind together to form the nucleus.  If you study nuclear chemistry long enough, you'll see that Einstein's famous equation, E = mc2, applies here.
 
The periodic table would predict 108 for the most stable silver isotope, but there are only two stable isotopes of silver and 108 isn't one of them.  Turns out the silver-107 and silver-109 are almost equally abundant, making the average atomic mass nearly 108.  Once you know that the two isotopes have masses of nearly 107 and 109, you can determine which one is more abundant using the 107.9 g/mol shown on the periodic table.  Because 107.9 is closer to 107 than it is to 109, then you know that silver-107 is slightly more abundant.  I hope this helps a bit.  I like the other two answers too.
There are two stable isotopes of silver
107Ag is 51.84% of all silver on the earth
109Ag is 48.16% of all silver on the earth
there are many other unstable isotopes.
I am not sure why you asked that question here because a simple web search would have given you that information.
 
The reasons the atomic weight is not an integer are twofold.
1) The atomic mass in the periodic table is the average mass of all silver.
So the masses of all the isotopes and what percent of each exist need to be taken into account to find the average value given in the periodic table.
And to a very very small extent,
2) The protons and neutrons each have an atomic mass of 1, but don't forget there are 47 electrons each with a very small mass.
The easiest way is to look up silver on a chart of the nuclides.  Lacking that, find the atomic number and weight of silver.  Which gives you 47 and 107.87.  You now know that Silver has 47 protons in the nucleus.
Rounding the weight up to a whole number gives 108.  Which suggests that silver has mostly 108-47 or 61 neutrons in the nucleus.  Problem is odd numbers of neutrons tend to be either radioactive or very rare.
Silver is most likely a mix of 60 and 62 neutron isotopes or Silver 107 and 109.
Assuming the amount of the other isotopes are zero or trivial can set up a mixing equation.
107x + 109(1.00-x) = 107.87
Now  it is just a matter of solving for x to determine which isotope is the larger fraction.