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Ch 37: The Foundations of Modern Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 37: The Foundations of Modern PhysicsProblema 20
Capitolo 37, Problema 20

Identify the isotope that is 11 times as heavy as ¹²C and has 18 times as many protons as ⁶Li . Give your answer in the form ᴬS, where S is the symbol for the element. See Appendix C: Atomic and Nuclear Data.

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Step 1: Start by identifying the mass of the isotope that is 11 times as heavy as ¹²C. The mass of ¹²C is 12 atomic mass units (amu). Multiply this by 11 to find the mass of the isotope: \( 11 \times 12 = 132 \ \text{amu} \).
Step 2: Next, determine the number of protons in the isotope. The problem states that the isotope has 18 times as many protons as ⁶Li. The number of protons in ⁶Li is 3 (since the atomic number of lithium is 3). Multiply this by 18: \( 18 \times 3 = 54 \ \text{protons} \).
Step 3: Use the periodic table to identify the element with 54 protons. The atomic number corresponds to the number of protons, and an atomic number of 54 corresponds to the element xenon (Xe).
Step 4: Combine the mass number (132) and the element symbol (Xe) to write the isotope in the form \( ^{A}S \), where \( A \) is the mass number and \( S \) is the element symbol. The isotope is \( ^{132}\text{Xe} \).
Step 5: Verify the solution by checking that the isotope satisfies both conditions: it is 11 times as heavy as ¹²C (mass = 132 amu) and has 18 times as many protons as ⁶Li (54 protons).

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Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, carbon-12 (¹²C) and carbon-14 (¹⁴C) are isotopes of carbon. Understanding isotopes is crucial for identifying elements based on their mass and nuclear properties.

Atomic Number and Mass

The atomic number of an element is the number of protons in its nucleus, which determines the element's identity. The mass number is the total number of protons and neutrons. In this question, knowing the relationship between the mass of isotopes and their atomic numbers is essential for identifying the correct isotope.
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Element Symbols

Element symbols are one- or two-letter abbreviations used to represent chemical elements on the periodic table. Each symbol is unique to an element and often derived from its English or Latin name. In this question, the final answer requires the correct symbol for the identified isotope, emphasizing the importance of recognizing and using these symbols accurately.
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