Question

Consider two isotopes Fe-54 and Fe-56. (a) Write the nuclear symbol for both isotopes. (b) How do they differ from each other?

Short answer

The nuclear symbols for the isotopes are: - Fe-54: $^{54}_{26}\textrm{Fe}$ - Fe-56: $^{56}_{26}\textrm{Fe}$ The main difference between these two isotopes is the number of neutrons in their nucleus. Fe-54 has 28 neutrons, while Fe-56 has 30 neutrons.

Step-by-step solution

(a) Nuclear Symbol for Isotopes Fe-54 and Fe-56

Isotopes are atoms of the same element but have different numbers of neutrons. They have the same atomic number (Z) but different mass numbers (A). To write the nuclear symbol for isotopes, we use the following format: $$ ^{A}_{Z}\textrm{X} $$ Where A is the mass number, Z is the atomic number, and X is the element symbol. For iron (Fe), its atomic number (Z) is 26. The given isotopes are Fe-54 and Fe-56, which means their mass numbers (A) are 54 and 56, respectively. Using the format mentioned above, the nuclear symbols for the isotopes are: $$ ^{54}_{26}\textrm{Fe},\ ^{56}_{26}\textrm{Fe} $$

(b) Differences between Fe-54 and Fe-56

Both Fe-54 and Fe-56 isotopes have the same atomic number (26), which means they have the same number of protons and electrons. The difference between these isotopes lies in their mass number (A), which represents the total number of protons and neutrons in the nucleus. Fe-54 has a mass number of 54, while Fe-56 has a mass number of 56. Subtracting the atomic number (26) from the mass numbers, we can determine the number of neutrons for each isotope: - $$\textrm{Neutrons in Fe-54} = 54 - 26 = 28$$ - $$\textrm{Neutrons in Fe-56} = 56 - 26 = 30$$ Therefore, the difference between the two isotopes is the number of neutrons. Fe-54 has 28 neutrons, while Fe-56 has 30 neutrons.

Key concepts

Nuclear Symbol

A nuclear symbol is a concise way to represent an atom's nucleus and provides essential information about the element. It uses the format \( ^{A}_{Z} \text{X} \), where:

• \( A \) is the mass number, indicating the total number of protons and neutrons.
• \( Z \) is the atomic number, which represents the number of protons.
• \( \text{X} \) is the chemical symbol of the element.

This symbol efficiently showcases both the identity of the element and its nuclear composition. For example, for iron, which has the chemical symbol "Fe" and an atomic number of 26, if it has mass numbers 54 and 56, the nuclear symbols would look like:

• For isotope Fe-54: \( ^{54}_{26} \text{Fe} \)
• For isotope Fe-56: \( ^{56}_{26} \text{Fe} \)

These representations underline the importance of understanding isotopes and their subtle differences.

Mass Number

The mass number of an atom is a crucial detail that tells you the total number of protons and neutrons within its nucleus. It's often denoted by the letter \( A \) in nuclear symbols. Unlike the atomic number, which defines the identity of an element, the mass number can vary even within atoms of the same element, giving rise to different isotopes. For example, in our isotopes of iron, Fe-54 and Fe-56, the mass numbers are 54 and 56 respectively. These numbers mean that:

• Fe-54 contains 54 protons and neutrons combined
• Fe-56 includes 56 protons and neutrons combined

This difference in mass number distinguishes isotopes as unique entities, each with a slightly different weight, but generally maintaining the same chemical behavior.

Neutrons

Neutrons play a key role in distinguishing isotopes of the same element, and they are neutral particles, meaning they carry no charge. To find out how many neutrons an isotope has, you subtract the atomic number from the mass number: \( ext{number of neutrons} = A - Z \).For example, examining the isotopes Fe-54 and Fe-56:

• For Fe-54: The mass number is 54. Subtract the atomic number 26 (number of protons), yielding 28 neutrons.
• For Fe-56: The mass number is 56. Subtract the atomic number 26, resulting in 30 neutrons.

Understanding the number of neutrons in each isotope allows scientists to understand the stability and reactions of those isotopes. Tiny differences, such as having 28 versus 30 neutrons, may affect atomic mass and nuclear properties without changing chemical properties significantly.