Textbook Question
A parallel-plate capacitor with a 1.0 mm plate separation is charged to 75 V. With what kinetic energy, in eV, must a proton be launched from the negative plate if it is just barely able to reach the positive plate?
1
views
Ch 37: The Foundations of Modern Physics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 37, Problem 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.
Verified step by step guidance1
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).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
Guided course
07:19
Moles & Avogadro's Number
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.
Recommended video:
Guided course
07:10Inductors in Circuits
Related Practice
Textbook Question
The factor γ appears in many relativistic expressions. A value γ = 1.01 implies that relativity changes the Newtonian values by approximately 1% and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is γ = 1.01 for (a) an electron, (b) a proton, and (c) an alpha particle?
2
views
Textbook Question
Express in eV (or keV or MeV if more appropriate): The kinetic energy of an electron moving with a speed of 5.0 x 10⁶ m/s .
1
views
Textbook Question
Consider the gold isotope 197Au. The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold nucleus?
Textbook Question
How many electrons, protons, and neutrons are contained in the following atoms or ions: (a) ¹⁰B, (b) ¹³N⁺, and (c) ¹⁷O⁺⁺⁺?
1
views
Textbook Question
What is the velocity, as a fraction of c, of an electron with 2.0 GeV total energy? Hint: This problem uses relativity.
1
views