Question

How do the isotopes of argon, \(\mathrm{Ar}-36, \mathrm{Ar}-38,\) and \(\mathrm{Ar}-40,\) differ from each other? Write the nuclear symbol for all three isotopes.

Short answer

Answer: The main differences between the three isotopes of argon are the number of neutrons in their nucleus, which are 18, 20, and 22 neutrons for Ar-36, Ar-38, and Ar-40, respectively. Their nuclear symbols are: - Ar-36: \[^{36}_{18}\textrm{Ar}\] - Ar-38: \[^{38}_{18}\textrm{Ar}\] - Ar-40: \[^{40}_{18}\textrm{Ar}\]

Step-by-step solution

Understand isotopes

Isotopes are different forms of the same element that have the same number of protons but a different number of neutrons in the nucleus of the atom. This means they have the same atomic number (Z) but a different mass number (A).

Identify the atomic number for Argon

Argon (Ar) is a chemical element with the atomic number (Z) of 18. This means that all isotopes of argon will have 18 protons in their nucleus.

Calculate the number of neutrons

The three isotopes of argon are Ar-36, Ar-38, and Ar-40. The mass number (A) of each isotope is given in the subscript, which is equal to the number of protons plus the number of neutrons (A = Z + N). For each isotope: - Ar-36: 36 = 18 + N, so N = 18 - Ar-38: 38 = 18 + N, so N = 20 - Ar-40: 40 = 18 + N, so N = 22

Write nuclear symbols

To write the nuclear symbol for each isotope, we need the chemical symbol (X) of the element, the atomic number (Z) on the lower left side of the symbol, and the mass number (A) on the upper left side of the symbol. In the case of argon isotopes: - Ar-36: \[^{36}_{18}\textrm{Ar}\] - Ar-38: \[^{38}_{18}\textrm{Ar}\] - Ar-40: \[^{40}_{18}\textrm{Ar}\]

Conclusion

The isotopes of argon, Ar-36, Ar-38, and Ar-40, differ from each other by the number of neutrons in their nucleus, which are 18, 20, and 22, respectively. The nuclear symbols for each isotope are: - Ar-36: \[^{36}_{18}\textrm{Ar}\] - Ar-38: \[^{38}_{18}\textrm{Ar}\] - Ar-40: \[^{40}_{18}\textrm{Ar}\]

Key concepts

Nuclear Symbol

The nuclear symbol is a succinct notation representing the atomic number, mass number, and chemical symbol of an isotope. It provides valuable information at a glance and is essentially the ID card of an atom. Let's break it down with argon as our example:

• The chemical symbol 'Ar' identifies the element as argon.
• The atomic number (18) is located at the lower left of the symbol, indicating the number of protons in the atom's nucleus.
• The mass number, varying for each isotope (36, 38, or 40 for argon), is placed at the upper left, representing the total number of protons and neutrons.

For the argon isotopes, we therefore see these symbols: \[^{36}_{18}\textrm{Ar}\], \[^{38}_{18}\textrm{Ar}\], and \[^{40}_{18}\textrm{Ar}\]. These symbols allow us to distinguish between isotopes quickly and are essential for understanding atomic structure and chemical reactions.

Atomic Number

The atomic number, often symbolized by the letter 'Z', represents the number of protons in the nucleus of an atom. It is a unique identifier for each element on the periodic table. For instance, argon has an atomic number of 18, which means every isotope of argon has 18 protons. No matter the number of neutrons, the atomic number remains constant across isotopes.

It's important to note that the chemical properties of an element are determined by its atomic number because it defines the element's electron configuration, which dictates how the element interacts with others.

Mass Number

A fundamental characteristic of isotopes is the mass number, which is denoted by 'A'. It reflects the total count of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number is not consistent across isotopes of the same element. For example, the mass numbers for argon isotopes are 36, 38, and 40, respectively.

• For \[^{36}_{18}\textrm{Ar}\], the mass number is 36.
• For \[^{38}_{18}\textrm{Ar}\], the mass number is 38.
• For \[^{40}_{18}\textrm{Ar}\], the mass number is 40.

This variety in mass numbers among isotopes leads to differences in atomic mass but not in chemical properties.

Neutrons in Atoms

Neutrons are subatomic particles in the nucleus of an atom, having no electric charge and thus often being referred to as 'neutral' particles. The number of neutrons is variable even among atoms of the same element, giving birth to different isotopes.

To find the number of neutrons in an isotope, subtract the atomic number from the mass number (N = A - Z). For argon isotopes:

• Ar-36 has 18 protons and 18 neutrons.
• Ar-38 contains 18 protons and 20 neutrons.
• Ar-40 possesses 18 protons and 22 neutrons.

These differences in neutron count affect the atomic mass and stability of isotopes but not their chemical behavior.