Question

Nuclei with the same mass number but different atomic numbers are called isobars. Consider Ca-40, Ca-41, K-41 and Ar-41. (a) Which of these are isobars? Which are isotopes? (b) What do \(\mathrm{Ca}-40\) and \(\mathrm{Ca}-41\) have in common? (c) Correct the statement (if it is incorrect): Atoms of \(\mathrm{Ca}-41, \mathrm{~K}-41\), and Ar-41 have the same number of neutrons.

Short answer

Is it true that Ca-41, K-41, and Ar-41 have the same number of neutrons? Answer: The isobars are Ca-41, K-41, and Ar-41, while the isotopes are Ca-40 and Ca-41. The common aspect between Ca-40 and Ca-41 is that they both share the same atomic number, i.e., they both have 20 protons. The given statement about Ca-41, K-41, and Ar-41 having the same number of neutrons is incorrect, as their number of neutrons are 21, 22, and 23 respectively.

Step-by-step solution

Define Isobars and Isotopes

Isobars are nuclei with the same mass number (total number of protons and neutrons) but different atomic numbers (number of protons). Isotopes are nuclei with the same atomic number and different mass numbers.

Identify Mass Number and Atomic Number for Each Element

The symbol notation A-Z tells us that the mass number (A) is the sum of the numbers of protons and neutrons in the nucleus, and the atomic number (Z) is the number of protons. The atomic numbers of the given elements are: - Ca (Calcium) has an atomic number Z = 20 - K (Potassium) has an atomic number Z = 19 - Ar (Argon) has an atomic number Z = 18 Now we can associate the mass numbers given for each nucleus: - Ca-40: A = 40, Z = 20 - Ca-41: A = 41, Z = 20 - K-41: A = 41, Z = 19 - Ar-41: A = 41, Z = 18

Identify Isobars and Isotopes

To find the isobars and isotopes among the given nuclei, we can use the definitions from the first step: - Isobars: Nuclei with the same mass number but different atomic numbers - Ca-41, K-41, and Ar-41 are isobars since they have the same mass number (A = 41) and different atomic numbers (Z = 20, 19, and 18, respectively). - Isotopes: Nuclei with the same atomic number and different mass numbers - Ca-40 and Ca-41 are isotopes since they have the same atomic number (Z = 20) and different mass numbers (A = 40 and 41, respectively).

Find the Common Aspect between Ca-40 and Ca-41

Ca-40 and Ca-41 are isotopes, which means they share the same atomic number, i.e., the same number of protons. Both of them have 20 protons.

Verify the Given Statement About Neutrons

The statement says that Ca-41, K-41, and Ar-41 have the same number of neutrons. To verify this, we'll calculate the number of neutrons for each by subtracting the atomic number (Z) from the mass number (A): - Number of neutrons in Ca-41: A - Z = 41 - 20 = 21 - Number of neutrons in K-41: A - Z = 41 - 19 = 22 - Number of neutrons in Ar-41: A - Z = 41 - 18 = 23 Comparing the number of neutrons, we can see that the given statement is incorrect, as all three nuclei have a different number of neutrons.

Key concepts

Isobars

Isobars are a fascinating concept in nuclear chemistry. These are nuclei that have the same mass number, meaning the total number of protons and neutrons is identical, but they differ in atomic numbers, which implies a different number of protons.
For example, in the case of Ca-41, K-41, and Ar-41, they all share a mass number of 41. However, they have different atomic numbers: 20 for calcium (Ca), 19 for potassium (K), and 18 for argon (Ar). This difference in the number of protons makes them different elements.

• Isobars can have different physical properties as they are different elements despite having the same mass number.
• Studying isobars helps chemists and physicists understand nuclear reactions and stability.

Due to their differing atomic composition, isobars can exhibit variance in chemical behavior and nuclear stability.

Isotopes

Isotopes, while sounding quite similar to isobars, are distinctly different. They refer to atoms of the same element which have the same number of protons, hence the same atomic number, but differ in the number of neutrons, giving them different mass numbers.
Taking calcium as an example, Ca-40 and Ca-41 are isotopes. Both have an atomic number of 20, meaning they each have 20 protons.

• The difference arises from their mass numbers: Ca-40 has 20 neutrons, while Ca-41 has 21 neutrons.
• Isotopes have nearly identical chemical behavior because they belong to the same element; however, their physical properties might differ, such as varying atomic masses or nuclear stability.

Isotopes are crucial in various scientific fields, including everything from radiocarbon dating to medical diagnostics.

Atomic Number

The atomic number is a fundamental concept in chemistry and physics. It is defined as the number of protons found in the nucleus of an atom, and it determines the element's identity.
For example, an atomic number of 20 corresponds to calcium (Ca). The atomic number is represented by the symbol 'Z'. It's important because it defines which element the atom is.

• Elements are arranged in the periodic table based on increasing atomic numbers.
• The atomic number also determines the number of electrons in a neutral atom, influencing chemical reactions and properties.

Understanding atomic numbers is essential for understanding the properties and interactions of elements in the periodic table.

Mass Number

The mass number is a key concept in understanding atomic and molecular structure. It is the total count of protons and neutrons in an atom's nucleus. The mass number, represented by 'A', differs from the atomic number, which only counts protons.
For instance, in Ca-41, the mass number is 41, consisting of 20 protons and 21 neutrons.

• The mass number is used to differentiate between isotopes of the same element.
• Although it provides the "heaviness" of an atom, the mass number is not the same as atomic mass, which is an average that considers isotopic distribution in nature.

Grasping the concept of mass number aids in understanding atomic structure, isotopes, and nuclear reactions.