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Ch 43: Nuclear Physics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 43: Nuclear PhysicsProblem 1
Chapter 42, Problem 1

How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, 01428Si^{28}_{\(\phantom{0}\)14}Si; (b) rubidium, 03785Rb^{85}_{\(\phantom{0}\)37}Rb; (c) thallium, 081205Tl^{205}_{\(\phantom{0}\)81}Tl?

Verified step by step guidance
1
Step 1: Understand the notation used for isotopes. The isotope notation is typically written as A/Z Element, where A is the mass number (total number of protons and neutrons), Z is the atomic number (number of protons), and 'Element' is the chemical symbol. For example, 01428Si^{28}_{14}Si represents silicon with a mass number of 28 and an atomic number of 14.
Step 2: Determine the number of protons in the nucleus. The atomic number (Z) directly gives the number of protons in the nucleus. For (a) silicon, Z = 14, so there are 14 protons. For (b) rubidium, Z = 37, so there are 37 protons. For (c) thallium, Z = 81, so there are 81 protons.
Step 3: Calculate the number of neutrons in the nucleus. The number of neutrons is given by subtracting the atomic number (Z) from the mass number (A). Use the formula: n=A-Z. For (a) silicon, n = 28 - 14 = 14 neutrons. For (b) rubidium, n = 85 - 37 = 48 neutrons. For (c) thallium, n = 205 - 81 = 124 neutrons.
Step 4: Summarize the findings for each isotope. For (a) silicon, the nucleus contains 14 protons and 14 neutrons. For (b) rubidium, the nucleus contains 37 protons and 48 neutrons. For (c) thallium, the nucleus contains 81 protons and 124 neutrons.
Step 5: Verify the calculations and ensure the understanding of isotope notation. Double-check the subtraction for neutrons and confirm the atomic numbers using a periodic table to ensure accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Structure

The atomic structure consists of protons, neutrons, and electrons. Protons and neutrons reside in the nucleus, while electrons orbit around it. The number of protons defines the element, while the number of neutrons can vary, leading to different isotopes of the same element.
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Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons. This difference in neutron count affects the atomic mass but not the chemical properties. For example, silicon-28 has 14 protons and 14 neutrons, while silicon-29 has 14 protons and 15 neutrons.

Nuclear Notation

Nuclear notation is a shorthand representation of an isotope, indicating the element's symbol, the number of protons (atomic number) as a subscript, and the total number of nucleons (protons + neutrons) as a superscript. For instance, in the notation ^{28}_{14}Si, 14 is the number of protons, and 28 indicates the total number of protons and neutrons.
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Related Practice
Textbook Question

(a) Is the decay n→p+β−+ve‾n\(\rightarrow\) p+\(\beta\)^{-}+\(\overline{v_{e}\)} energetically possible? If not, explain why not. If so, calculate the total energy released.

(b) Is the decay n→p+β++ve‾n\(\rightarrow\) p+\(\beta\)^{+}+\(\overline{v_{e}\)} energetically possible? If not, explain why not. If so, calculate the total energy released.

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Textbook Question

The most common isotope of uranium, 92238U_{92}^{238}U, has atomic mass 238.050788238.050788 u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

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Textbook Question

Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced by photons with frequency 22.722.7 MHz?

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