Problem 25 - Chemistry The Molecular Science

Question

Give the complete symbol \({ }_{Z}^{A} \mathrm{X}\) for each of these atoms: (a) nitrogen with 8 neutrons, (b) zinc with 34 neutrons, and (c) xenon with 75 neutrons.

Step-by-Step Solution

Answer

(a) \( {}_{7}^{15} \mathrm{N} \), (b) \( {}_{30}^{64} \mathrm{Zn} \), (c) \( {}_{54}^{129} \mathrm{Xe} \).

Step 1: Identify Proton Number (Z)

The proton number, or atomic number \( Z \), is the number of protons in an atom. For: (a) Nitrogen, \( Z = 7 \) (b) Zinc, \( Z = 30 \) (c) Xenon, \( Z = 54 \).

Step 2: Determine Mass Number (A)

The mass number \( A \) is the sum of protons and neutrons. (a) Nitrogen: \( A = 7 + 8 = 15 \) (b) Zinc: \( A = 30 + 34 = 64 \) (c) Xenon: \( A = 54 + 75 = 129 \).

Step 3: Write Complete Symbol

Use \({ }_{Z}^{A} \mathrm{X}\) to represent each atom: (a) \( {}_{7}^{15} \mathrm{N} \) (b) \( {}_{30}^{64} \mathrm{Zn} \) (c) \( {}_{54}^{129} \mathrm{Xe} \).

Key Concepts

Proton Number

The proton number, often denoted by the symbol \( Z \), is a fundamental property of an atom. It represents the number of protons in the nucleus of an atom, which defines the element's identity on the periodic table. For example, nitrogen, an essential element in biology, always has a proton number of 7. This means every nitrogen atom possesses exactly seven protons. Likewise, zinc, known for its anti-corrosive properties, has 30 protons, and xenon, a noble gas, carries 54 protons within its nucleus. These integer values are critical because they determine the chemical behavior of each element.

To easily identify an atom based on its proton number, consider its position on the periodic table. Elements are arranged in increasing order of their \( Z \) value, starting from hydrogen with \( Z = 1 \) at the top left, moving across each period and down each group. Hence, understanding the proton number unlocks the ability to predict an atom's elemental identity quickly.

Mass Number

Another vital atomic characteristic is the mass number, denoted by \( A \). It is the total count of an atom's protons and neutrons. While the proton number \( Z \) alone defines what element an atom is, the mass number helps differentiate between isotopes of the same element.

The mass number is determined by summing up the protons and neutrons in the atom's nucleus. Let's look at nitrogen as an example: if a nitrogen atom contains 8 neutrons, then its mass number will be \( 7 + 8 = 15 \). For zinc with 34 neutrons, the value would be \( 30 + 34 = 64 \). Finally, a xenon atom containing 75 neutrons will have a mass number of \( 54 + 75 = 129 \).

Notice that mass numbers are not listed on the periodic table, as they vary with different isotopes. It’s essential to understand that while all atoms of a single element share the same proton number, their mass numbers can differ due to the number of neutrons.

Neutrons

Neutrons are neutral particles found in an atom's nucleus, playing a crucial role in stabilizing the atomic structure. Unlike protons, neutrons do not carry any charge, which prevents them from influencing the atom's chemical properties. However, they significantly impact the mass of the atom.

The neutron count in an atom can vary without changing the element itself. This variance results in different isotopes of the same element. For instance, the element nitrogen may have 7 or 8 neutrons in its isotopes. Each variation changes the mass but not the elemental properties of nitrogen.

Calculating the number of neutrons in an atom is straightforward: simply subtract the proton number \( Z \) from the mass number \( A \). For instance,

• Nitrogen with a mass number of 15 has \( 15 - 7 = 8 \) neutrons.
• Zinc with \( A = 64 \) contains \( 64 - 30 = 34 \) neutrons.
• Xenon with \( A = 129 \) comprises \( 129 - 54 = 75 \) neutrons.

This counting method confirms the isotopes correctly, providing each a unique atomic identity despite sharing the same element designation.