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Chapter 2: Problem 15

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

Expert verified
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

01

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.
02

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
03

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).
04

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.
05

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.

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