Question

See the definition for isobars in Question 15. Consider \(\mathrm{Cr}-54, \mathrm{Fe}-54, \mathrm{Fe}-58,\) and \(\mathrm{Ni}-58\) (a) Which of these are isobars? Which are isotopes? (b) What do Fe-54 and Fe-58 have in common? (c) Which atoms have the same number of neutrons?

Short answer

Question: Identify the isobars, isotopes, commonalities between Fe-54 and Fe-58, and atoms with the same number of neutrons among the given elements: Chromium-54 (Cr-54), Iron-54 (Fe-54), Iron-58 (Fe-58), and Nickel-58 (Ni-58). Answer: Isobars: Cr-54 and Fe-54 (atomic mass number 54), Fe-58 and Ni-58 (atomic mass number 58); Isotopes: Fe-54 and Fe-58 (both Iron with 26 protons); Fe-54 and Fe-58 commonality: same atomic number (26 protons); Atoms with the same number of neutrons: Cr-54 and Ni-58 (30 neutrons).

Step-by-step solution

(a) Identifying Isobars and Isotopes

To find isobars among the given elements, we need to identify those with the same atomic mass number (total number of protons and neutrons). To find isotopes, we should identify those with the same atomic number (protons). The given isotopes include: 1. Chromium-54 (Cr-54): 24 protons and 54 - 24 = 30 neutrons 2. Iron-54 (Fe-54): 26 protons and 54 - 26 = 28 neutrons 3. Iron-58 (Fe-58): 26 protons and 58 - 26 = 32 neutrons 4. Nickel-58 (Ni-58): 28 protons and 58 - 28 = 30 neutrons Isobars: 1. Cr-54 and Fe-54: both have an atomic mass number of 54 2. Fe-58 and Ni-58: both have an atomic mass number of 58 Isotopes: 1. Fe-54 and Fe-58: both are isotopes of Iron (Fe) with the same atomic number (26 protons)

(b) Fe-54 and Fe-58 Commonality

Both Fe-54 and Fe-58 have the same atomic number, which is 26 protons. This means that they are isotopes of the same element, Iron (Fe).

(c) Atoms with the Same Number of Neutrons

Comparing the number of neutrons in each isotope: 1. Chromium-54 (Cr-54): 30 neutrons 2. Iron-54 (Fe-54): 28 neutrons 3. Iron-58 (Fe-58): 32 neutrons 4. Nickel-58 (Ni-58): 30 neutrons Cr-54 and Ni-58 have the same number of neutrons, which is 30.

Key concepts

Atomic Mass Number

The atomic mass number is a fundamental concept in chemistry and physics, representing the total number of protons and neutrons in an atom's nucleus. It's crucial for distinguishing different kinds of atoms, especially when exploring isobars—atoms of different elements that have the same atomic mass number but different atomic numbers.

For example, in the exercise comparing Chromium-54 (Cr-54) and Iron-54 (Fe-54), both have an atomic mass number of 54, though they are different elements. This is what makes them isobars. The atomic mass number, therefore, helps us understand why atoms can have the same mass but differ in their elemental form.

Atomic Number

The atomic number, which is denoted by the symbol Z, defines the identity of an element by giving the number of protons in an atom's nucleus. In the isotopes of Iron (Fe-54 and Fe-58) from the exercise, both share the same atomic number of 26, which classifies them as isotopes of the element iron.

Understanding the atomic number is key to predicting the chemical properties of an element, as it directly determines the element's placement in the periodic table. Additionally, since each element has a unique atomic number, it serves as a universal identifier for that element.

Neutrons in Isotopes

Neutrons play a significant role in isotopes, as they contribute to the atomic mass number but, unlike protons, do not affect the atomic number. Isotopes of an element have the same number of protons but vary in the number of neutrons.

In the given exercise, Chromium-54 (Cr-54) and Nickel-58 (Ni-58) have 30 neutrons each, despite being different elements. This shared neutron count does not make them isotopes because isotopes refer to atoms of the same element with different neutron counts. Recognizing that neutrons determine the mass of isotopes is imperative when studying atomic structure and nuclear reactions.