Question

For the noble gases (the Group 8 A elements) \({ }_{2}^{4}\) He, \({ }_{10}^{20}\) Ne, \({ }_{18}^{40} \mathrm{Ar},{ }_{36}^{84} \mathrm{Kr},\) and \({ }_{54}^{132} \mathrm{Xe},\) (a) determine the number of protons and neutrons in the nucleus of each atom, and (b) determine the ratio of neutrons to protons in the nucleus of each atom. Describe any general trend you discover in the way this ratio changes with increasing atomic number.

Short answer

Each noble gas has a higher neutron-to-proton ratio with increasing atomic number.

Step-by-step solution

Determine Protons

For each noble gas atom, the number of protons is equal to its atomic number. Thus, for He, Ne, Ar, Kr, and Xe, the number of protons are 2, 10, 18, 36, and 54, respectively.

Calculate Neutrons

To find the number of neutrons, subtract the atomic number from the atomic mass number. For He (4 - 2 = 2), Ne (20 - 10 = 10), Ar (40 - 18 = 22), Kr (84 - 36 = 48), and Xe (132 - 54 = 78). So, the number of neutrons for He, Ne, Ar, Kr, and Xe are 2, 10, 22, 48, and 78, respectively.

Neutron-to-Proton Ratio

To find the neutron-to-proton ratio, divide the number of neutrons by the number of protons for each element: - He: 2/2 = 1 - Ne: 10/10 = 1 - Ar: 22/18 = 1.22 - Kr: 48/36 = 1.33 - Xe: 78/54 = 1.44

Identify the Trend

As the atomic number increases (from He to Xe), the neutron-to-proton ratio also increases. This indicates that heavier noble gases have more neutrons per proton compared to lighter ones.

Key concepts

Atomic Number

In the world of chemistry, the term "atomic number" is pivotal, especially when discussing elements like the noble gases. The atomic number is the number that corresponds to the total count of protons in an atom's nucleus. For noble gases, this is represented as

• Helium (He): 2
• Neon (Ne): 10
• Argon (Ar): 18
• Krypton (Kr): 36
• Xenon (Xe): 54

Understanding the atomic number gives us insight into an element's position on the periodic table. It also reveals the element's basic properties. For noble gases, this means a complete outer electron shell, contributing to their chemical inertness. Always remember, the atomic number is unique to each element and defines its identity.

Protons

Protons are subatomic particles with a positive charge, residing in the nucleus of an atom. Their number is equal to the atomic number, making them fundamental in determining the identity of an element. In noble gases:

• Helium has 2 protons
• Neon has 10 protons
• Argon has 18 protons
• Krypton has 36 protons
• Xenon has 54 protons

These protons not only define the element but also influence its atomic mass when combined with neutrons. Noble gases, with their stable atomic structures, reflect a balance that protons help maintain. This balance is key to their lack of reactivity and stability under normal conditions.

Neutrons

Neutrons are electrically neutral particles, playing a crucial role in the nucleus alongside protons. They don't affect the chemical properties directly, as electrons and protons do, but they impact the atomic mass. For the noble gases:

• Helium has 2 neutrons
• Neon has 10 neutrons
• Argon has 22 neutrons
• Krypton has 48 neutrons
• Xenon has 78 neutrons

Neutrons help stabilize the nucleus. If their number becomes too high or too low relative to protons, the atom can become unstable. For noble gases, maintaining an optimal number of neutrons ensures atomic stability. This feature is significant as the atomic number increases, often requiring additional neutrons to uphold nucleus cohesion.

Neutron-to-Proton Ratio

The neutron-to-proton ratio is a concept that reveals the stability and nature of the nucleus in an atom. By dividing the number of neutrons by the number of protons, we can understand this ratio better:

• Helium: 1
• Neon: 1
• Argon: 1.22
• Krypton: 1.33
• Xenon: 1.44

This increasing ratio as we move from helium to xenon highlights how atoms with higher atomic numbers need more neutrons to achieve stability. Heavier atoms, thus, often have a higher neutron-to-proton ratio. The trend in noble gases reflects this, as more neutrons are necessary to counterbalance the repulsion between additional protons.