Question

Write the correct symbol, with both superscript and subscript, for each of the following. Use the list of elements inside the front cover as needed: (a) the isotope of platinum that contains 118 neutrons, (b) the isotope of krypton with mass number 84, (c) the isotope of arsenic with mass number \(75,(\mathrm{~d})\) the isotope of magnesium that has an equal number of protons and neutrons.

Short answer

The correct symbols for the given isotopes are: (a) \[ \, _{78}^{196} \textrm{Pt} \] (b) \[ \, _{36}^{84} \textrm{Kr} \] (c) \[ \, _{33}^{75} \textrm{As} \] (d) \[ \, _{12}^{24} \textrm{Mg} \]

Step-by-step solution

Identify the atomic number

From the list of elements, the atomic number for platinum (Pt) is 78.

Calculate the mass number

The mass number, A, is the sum of the number of protons and neutrons. Since Platinum has 118 neutrons, A = Protons (Atomic number) + Neutrons = 78 + 118 = 196

Write the symbol

The symbol for the platinum isotope with 118 neutrons is: \[ \, _{78}^{196} \textrm{Pt} \] (b) Isotope of krypton with mass number 84

Identify the atomic number

From the list of elements, the atomic number for krypton (Kr) is 36.

Write the symbol

The symbol for the krypton isotope with a mass number of 84 is: \[ \, _{36}^{84} \textrm{Kr} \] (c) Isotope of arsenic with mass number 75

Identify the atomic number

From the list of elements, the atomic number for arsenic (As) is 33.

Write the symbol

The symbol for the arsenic isotope with a mass number of 75 is: \[ \, _{33}^{75} \textrm{As} \] (d) Isotope of magnesium with an equal number of protons and neutrons

Identify the atomic number

From the list of elements, the atomic number for magnesium (Mg) is 12.

Calculate the mass number

Since magnesium has an equal number of protons and neutrons, and there are 12 protons, there are also 12 neutrons. A = Protons (Atomic number) + Neutrons = 12 + 12 = 24

Write the symbol

The symbol for the magnesium isotope with an equal number of protons and neutrons is: \[ \, _{12}^{24} \textrm{Mg} \]

Key concepts

Atomic Number

The atomic number, often represented by the symbol \( Z \), is a fundamental property of an element, defining the element’s identity. It represents the number of protons in the nucleus of an atom.
Each element on the periodic table has a unique atomic number, and it essentially determines which element you're dealing with.
Here are some key facts about atomic numbers:

• The atomic number is used to uniquely identify chemical elements.
• Each element's properties and placement in the periodic table are influenced by its atomic number.
• The atomic number is equal to the number of protons in an atom's nucleus. For a neutral atom, it's also equal to the number of electrons surrounding the nucleus.

For example, Platinum (Pt) has an atomic number of 78, meaning it has 78 protons. Similarly, Krypton (Kr) has an atomic number of 36, and Arsenic (As) has 33.
Knowing this number enables one to determine an element’s chemical properties and its place on the periodic table.

Mass Number

The mass number, denoted by the symbol \( A \), is the total count of protons and neutrons in an atom's nucleus.
Unlike the atomic number, the mass number is not unique to each element because elements can have different isotopes.
Here are some important points about mass numbers:

• The mass number provides information about the isotope of an element.
• It is simply the sum of protons and neutrons in the nucleus.
• Mass number does not appear on the periodic table because it varies among isotopes of a particular element.

For instance, the isotope of platinum with 118 neutrons has a mass number of 196, calculated as \( A = 78 + 118 \).
Thus, knowing the mass number helps in identifying the specific isotope of an element and its nuclear characteristics.

Neutrons

Neutrons are one of the fundamental particles that make up the atom’s nucleus, alongside protons.
They play a crucial role in the stability of the nucleus and in the formation of isotopes.
Here's what you need to know about neutrons:

• Neutrons are uncharged particles, which means they carry no electrical charge.
• Together with protons, they contribute to the mass of the atom.
• The number of neutrons can vary within atoms of the same element, leading to different isotopes.
• For a stable atom, the number of neutrons is often similar to the number of protons, although this is not a strict rule for all elements.

In the case of magnesium, if it has an equal number of protons and neutrons (12 each), it forms an isotope with a mass number of 24.
Understanding the role of neutrons is crucial for grasping how isotopes occur and how they differ from the usual atomic form of elements.