mass = molar mass/Avogadro's number
or
m = M/NA
where:
mass is [g/molecule]
molar mass is [g/mol]
Avogadro's number is [molecules/mol] = 6.022 x 1023
Therefore, the values that are given in the periodic table, such as 1.008 for Hydrogen, are in [g/mol], because they are molar masses.
The unit chosen for atomic masses is 1/12 the mass of an atom of carbon-12, which is defined to have a mass of exactly 12. This unit is called a universal atomic mass unit and its symbol is u (or amu). For example, the mass of an atom of lithium-7 is 7.016003 u; that is, an atom of lithium-7 is 7.016003 times as massive as 1/12 the mass of an atom of carbon-12. Lithium-7 has 4 neutrons and 3 protons. The isotope of Lithium-7 is Lithium-6, where Lithium-6 has 3 protons and 3 neutrons. Typically, if the number of neutrons in an element are altered, it is still the same element. Only if the number of protons in an element changes, does the element change. The element numbers are actually based on the number of protons in each element. If the number of electrons in an element change then the charge of an element is changed. If the number of protons equal the number of electrons in an atom then the atom is stable. If the number of electrons exceed the number of protons in an element, then the element has a negative charge. If the number of electrons are less then the number of protons in an element, then the element has a positive charge. Sometimes molecules (made up of two or more atoms) can share electrons to create stability.
The atomic mass unit is fairly equal to the number of particles in an element, where particles are either neutrons or protons.
The numbers in the periodic table are atomic masses.
The atomic number in the periodic table for each element is the smaller number, the larger number is the atomic weight.
Typically, by rounding the atomic weight for any element to the largest whole number represents the total number of protons and neutrons per atom of each element.
1 u = 1 gram/mole
1 u = Mu/NA
where:
Mu is the molar mass constant
NA is Avogadro's constant
1 g = (Avogadro's number)*(number of atomic mass units)
unified atomic mass unit = atomic mass unit = universal mass unit = universal atomic mass unit
atomic mass unit is a relative measure, with respect to 1/12 the mass of carbon-12. Because atomic masses are relative masses, they are pure numbers and are sometimes given without units.
All elements are isotopes, the isotopes in the periodic table are the most naturally occuring and most abundand isotopes for each element.
How to determine the number of grams per mole for something?
Well, for an atom or molecule take the total atomic weight, that is the number of grams per mole for whatever is under consideration.
If one molecule is 18 u, where u is atomic mass unit, then 1 molecule has 18 particles, where the particles are neutrons and protons (particle 
proton neutron). The mass of 6.02 x 1023 molecules = 18 grams.
Therefore, 6.02 x 1023 atomic mass unuits = 1 gram.
or,
6.02 x 1023 particles = 1 gram
Related
▪ L - Mole