Question

Which of the following symbols represent isotopes of the same element? Explain. (a) \({ }_{9}^{19} X\) (b) \({ }_{10}^{19} X\) (c) \({ }_{9}^{21} X\) (d) \(\frac{21}{12} X\)

Short answer

(a) and (c) are isotopes.

Step-by-step solution

Understanding Isotopes

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. They have the same atomic number (denoted as the lower number in the nuclear symbol) but different mass numbers (the upper number).

Analyze Each Option

Each symbol in the options is given as \({ }_{Z}^{A} X\), where \(Z\) is the atomic number and \(A\) is the mass number. Let's identify the atomic numbers for each option: (a) \({ }_{9}^{19} X\) has atomic number 9.(b) \({ }_{10}^{19} X\) has atomic number 10.(c) \({ }_{9}^{21} X\) has atomic number 9.(d) \({ }_{12}^{21} X\) (interpreting \(\frac{21}{12} X\) as \({ }_{12}^{21} X\)) has atomic number 12.

Identify Isotopes

To be isotopes, symbols must have the same atomic number \(Z\). Comparing the atomic numbers: - \(a\) and \(c\) both have atomic number \(9\). - \(b\) and \(d\) have different atomic numbers \(10\) and \(12\) respectively.Thus, options (a) \({ }_{9}^{19} X\) and (c) \({ }_{9}^{21} X\) represent isotopes.

Key concepts

Atomic Number

The atomic number is a fundamental property of an element that defines its identity. It represents the number of protons present in the nucleus of an atom. Since protons carry a positive charge, the atomic number also determines the charge of the nucleus and, consequently, the number of electrons in a neutral atom. These electrons dictate the chemical behavior of the element.
When looking at isotopes, the atomic number remains constant. This is crucial since isotopes are different forms of the same element. For example:

• In option (a) \(_{9}^{19}X\), the atomic number is 9, indicating the element is fluorine.
• In option (b) \(_{10}^{19}X\), the atomic number is 10, identifying a different element, neon.
• For option (c) \(_{9}^{21}X\), the atomic number again is 9, reaffirming it is fluorine.

This distinct atomic number helps identify that (a) and (c) are isotopes of the same element, fluorine, despite having different mass numbers.

Mass Number

Mass number is another critical concept when discussing isotopes. It is the sum of protons and neutrons in an atom's nucleus, generally represented as the upper number in the isotope symbol. The mass number helps differentiate isotopes, as isotopes of an element have the same atomic number but different mass numbers.
For instance:

• Option (a) \(_{9}^{19}X\) has a mass number of 19. This means it has 19 nucleons (protons + neutrons) all together.
• Option (c) \(_{9}^{21}X\) has a mass number of 21, indicating 21 nucleons.

The different mass numbers between these isotopes reflect a change in the number of neutrons, while the number of protons (atomic number) remains unchanged. This results in isotopes of fluorine, with different physical properties but the same chemical behavior.

Neutrons

Neutrons play a key role in nuclear stability and define isotopes. They are neutral particles in the atomic nucleus that, along with protons, contribute to the mass number. Importantly, while isotopes of an element share the same atomic number, they differ in the number of neutrons, leading to changes in mass.
Consider the following examples based on mass number calculations:

• For option (a) \(_{9}^{19}X\), the number of neutrons can be calculated as \(19 - 9 = 10\).
• For option (c) \(_{9}^{21}X\), there are \(21 - 9 = 12\) neutrons.

By having different neutron counts, these forms \(_{9}^{19}X\) and \(_{9}^{21}X\) are isotopes. These variations in neutron numbers affect the atomic mass and sometimes stability, providing isotopes with slightly different physical properties.