Problem 9 - Chemistry for Allied Health

Question

A certain atom has an atomic number of 36 and a mass number of 84 . Write out the designation for this isotope in both nuclide symbol form and in hyphenated form.

Step-by-Step Solution

Answer

The nuclide symbol is \( \text{^84_{36}Kr} \) and the hyphenated form is Krypton-84.

Step 1: Understand the Definitions

The atomic number of an element, denoted as Z, is the number of protons in the nucleus. The mass number, usually denoted as A, is the sum of the number of protons and neutrons in the nucleus. Using these definitions, you can identify the element.

Step 2: Identify the Element

Using the periodic table, locate the element with atomic number 36. This number corresponds to the number of protons. The atomic number 36 is assigned to the element Krypton (Kr).

Step 3: Calculate Neutron Number

Calculate the number of neutrons (N) using the equation: \[ N = A - Z \] where A is the mass number, and Z is the atomic number. Substitute the given values: \[ N = 84 - 36 = 48 \].

Step 4: Write the Nuclide Symbol

The nuclide symbol is written in the form \( \text{^A_Z ext{Element}} \), where A is the mass number and Z is the atomic number. For this isotope:\[ \text{^84_{36}Kr} \].

Step 5: Write the Hyphenated Form

The hyphenated form is written as the name of the element followed by its mass number. For Krypton with a mass number of 84, this is written as Krypton-84.

Key Concepts

Atomic Number

The atomic number is a fundamental concept when it comes to understanding elements and their isotopes. It's represented by the symbol \( Z \) and denotes the number of protons found in the nucleus of an atom. Each element on the periodic table has a unique atomic number. This number essentially defines the identity of an element.

For example, the atomic number of Krypton is 36. This means every atom of Krypton has 36 protons in its nucleus. The atomic number is crucial for identifying elements because it determines the chemical properties of the element and where it is placed on the periodic table. The atomic number also equals the number of electrons in a neutral atom, maintaining a balanced charge.

Mass Number

Mass number, represented by \( A \), is the total count of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number isn't unique for each element due to the existence of isotopes. Isotopes are atoms of the same element (same \( Z \)) but with different numbers of neutrons, leading to different mass numbers.

To calculate the mass number, you simply add the number of protons and neutrons together:

• Protons (Atomic number, \( Z \))
• Neutrons (determined by \( N = A - Z \))

For Krypton, with an atomic number of 36 and a mass number of 84, you can find that the number of neutrons is 48 using the formula \( N = A - Z \). Therefore, the atom consists of 36 protons and 48 neutrons in its nucleus.

Nuclide Symbol

The nuclide symbol is a concise way to represent specific isotopes of an element. It includes information about the atomic number, mass number, and the element's symbol. The general format for a nuclide symbol is \( \text{^A_Z Element Symbol} \, \), where:

• \( A \) is the mass number
• \( Z \) is the atomic number
• Element Symbol represents the symbol for the element

In the case of the isotope of Krypton with a mass number of 84 and an atomic number of 36, the nuclide symbol is denoted as \( \text{^84_{36}Kr} \, \). This notation effectively communicates all the necessary nuclear information about that particular isotope.
Moreover, isotopes can be presented in a hyphenated form where the element name is followed by its mass number. For example, this isotope is also referred to as Krypton-84. This is a more casual way to refer to isotopes but is equally important in identifying the specific atom based on its nuclear composition.