Step 1: Understand the definition of isotopes.
Isotopes are atoms of the same element that have the same number of protons (and thus the same atomic number) but different numbers of neutrons. This difference in neutrons results in different mass numbers. For an element, the atomic number (Z) is fixed.
Step 2: Recall the atomic number of Chlorine (Cl).
Chlorine (Cl) has an atomic number of 17. This means all isotopes of chlorine must have 17 protons.
Step 3: Analyze the common isotopes of Chlorine.
The most common isotopes of chlorine are Chlorine-35 ($^{35}\text{Cl}$) and Chlorine-37 ($^{37}\text{Cl}$).
$^{35}\text{Cl}$ has 17 protons and $35 - 17 = 18$ neutrons.
$^{37}\text{Cl}$ has 17 protons and $37 - 17 = 20$ neutrons.
Both have the same atomic number (17) but different mass numbers (35 and 37), which fits the definition of isotopes.
Step 4: Evaluate the given options.
(1) Chlorine. $^{34\text{Cl}$ and $^{37}\text{Cl}$:} While $^{34}\text{Cl}$ is an isotope, $^{35}\text{Cl}$ and $^{37}\text{Cl}$ are the most prevalent and typically referred to common stable isotopes. However, fundamentally, $^{34}\text{Cl}$ and $^{37}\text{Cl}$ would also be isotopes of chlorine as long as they both have 17 protons. But when asked for "correct isotopes," it usually refers to the most recognized or stable ones.
(2) Chlorine. $^{35\text{Cl}$ and $^{36}\text{Cl}$:} $^{36}\text{Cl}$ is a radioactive isotope of chlorine. This pair shows two isotopes.
(3) Chlorine. $^{35\text{Cl}$ and $^{37}\text{Cl}$:} This pair represents the two most abundant and stable natural isotopes of chlorine. They both have the same atomic number (17) but different mass numbers (35 and 37). This is a correct pair of isotopes.
(4) Chlorine. $^{35\text{Cl}$ and $^{35}\text{Cl}$:} This represents the same isotope, not a pair of different isotopes.
Step 5: Select the best fit.
Among the given options, the pair $^{35}\text{Cl}$ and $^{37}\text{Cl}$ is the most commonly recognized and correct example of naturally occurring isotopes of Chlorine.
(3) Chlorine. $^{35\text{Cl}$ and $^{37}\text{Cl}$}