Are called isotopes two atoms (or ions) that have the same number of protons but different numbers of neutrons.
Isotopes therefore have the same atomic number Z (and the same symbol), but mass numbers A are different
.Example
On earth we find the following isotopes of iron: $_{26}^{53}Fe$ , $_{26}^{56}Fe$ , $_{26}^{57}Fe$ and $_{26}^{58}Fe$
As isotopes have the same number of protons, thus the same number electrons, and as electrons determine properties of chemicals, we can say that two isotopes have almost identical chemical properties. Two isotopes allow themselves to be separated by chemical reactions. During the history of the earth no chemical reaction has been able to differentiate between isotopes of an element. That's why these isotopes are found distributed with the same percentage throughout the earth. Some elements normally involved in the biochemistry of our body (eg iodine in the gland thyroid) have isotopes that are radioactive and harmful for the organism. Our body can not differentiate between "normal" isotope and radioactive isotope, it incorporates the nuisible isotope with the normal isotope, if given the opportunity.
Now the chemical element has to be redefined:
A chemical element is the set of atoms with the same atomic number.
An element therefore includes all isotopes of the same atomic number Z, all those atoms have the same chemical properties and the same symbol!
Example
The element chlorine has the isotopes $_{17}^{35}Cl$ $_{17}^{37}Cl$ They are the only atoms with Z=17 which exist.
Mass of one mole of nucleons (protons or neutrons): As the mass of a $p^+$ or $n^o$ is approximately $\frac{1}{6\cdot10^{23}}\;g$, a mole of $p^+$ or $n^o$ has an approximate mass of $\frac{1}{6\cdot 10^{23}}6\cdot 10^{23}$ $=$ $1\;g$
Mass of one mole of atoms from an isotope An isotope has A (= its mass number) nucleons, so one mole of atoms of an isotope has a mass of A$\cdot1=$A$\;g$.
Example
One mole of $_{26}^{53}Fe$ has for example a mass of $53\cdot 1$ $ =$ $ 53$ g
Atomic mass of a chemical element (= mass of one mole of atoms of this element) Elements are often made up of several isotopes occurring on earth with different percentages, so:
The atomic mass of an element is the average mass of one mole of its isotopes taking into account their respective percentages on earth.
Example
The chlorine isotopes that exist on earth are involved with the following percentages: $_{17}^{35}Cl$ : $(75.78\%)$ and $_{17}^{37}Cl$ : $(24.22\%)$ We have therefore: M(Cl) = Atomic mass of chlorine = Mass of one mole of Cl atoms = Mass of $\frac{75.78}{100}$ mol $_{17}^{35}Cl$ + mass of $\frac{24.22}{100}$ mol $_{17}^{37}Cl$ $=$ $\frac{75.78}{100}\cdot35$ $+$ $\frac{24.22}{100}\cdot 37$ $\approx$ $35.48\frac{g}{mol}$