Understanding Isotopes

Isotopes are atoms of the same chemical element that have the same number of protons in their nucleus but differ in the number of neutrons. Because they have the same number of protons, isotopes of an element always have the same atomic number (Z). The difference in the number of neutrons results in different mass numbers (A), which is the sum of protons and neutrons.

Analyzing Chlorine Isotopes

The question asks to identify the two isotopes of elemental chlorine. The atomic number for chlorine is 17. This means any isotope of chlorine must have 17 protons, and therefore, the subscript (Z) in its notation must be 17. The superscript represents the mass number (A).

Let's examine the given options:

• Option 1: \(^{35}_{17}C\) and \(^{36}_{17}C\). Both notations have the subscript 17, indicating the same atomic number. The mass numbers are 35 and 36, which are different. These represent isotopes based on the definition.
• Option 2: \(^{34}_{17}C\) and \(^{36}_{18}C\). The first notation has Z=17, while the second has Z=18. Since the atomic numbers are different, these cannot be isotopes of the same element.
• Option 3: \(^{35}_{17}C\) and \(^{37}_{17}C\). Both notations have the subscript 17, indicating the same atomic number (17 protons). The mass numbers are 35 and 37, which are different. This pair correctly represents isotopes of chlorine.
• Option 4: \(^{35}_{17}C\) and \(^{37}_{18}C\). The first notation has Z=17, while the second has Z=18. Since the atomic numbers are different, these are not isotopes of the same element.

Note: The standard chemical symbol for chlorine is 'Cl', not 'C' as used in the options. However, the atomic number (17) consistently identifies the element as chlorine.

Identifying the Correct Isotope Pair

Based on the definition of isotopes (same atomic number Z, different mass number A), the pair that fits this criterion for chlorine (Z=17) is \(^{35}_{17}C\) and \(^{37}_{17}C\).

Explanation:

• \(^{35}_{17}C\) has 17 protons and 35 - 17 = 18 neutrons.
• \(^{37}_{17}C\) has 17 protons and 37 - 17 = 20 neutrons.

Both atoms have 17 protons, confirming they are the same element (chlorine), and they have different numbers of neutrons (18 and 20), resulting in different mass numbers (35 and 37). Therefore, they are isotopes.