Ch 37: The Foundations of Modern Physics

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 37: The Foundations of Modern Physics

Problem 32

Chapter 37, Problem 32

The fission process n + ²³⁵U → ²³⁶U → ¹⁴⁴Ba + ⁸⁹Kr + 3n converts 0.185 u of mass into the kinetic energy of the fission products. What is the total kinetic energy in MeV?

Verified step by step guidance

Step 1: Understand the problem. The fission process converts a mass of 0.185 u into kinetic energy. We need to calculate the total kinetic energy in MeV using Einstein's mass-energy equivalence formula.

Step 2: Recall Einstein's mass-energy equivalence formula:

E = mc^2

, where

E

is the energy,

m

is the mass, and

c

is the speed of light. In this case, the mass

m

is given in atomic mass units (u), and we need to convert it into energy in MeV.

Step 3: Use the conversion factor: 1 atomic mass unit (u) is equivalent to 931.5 MeV/c². Therefore, the energy can be calculated as

E = (0.185 \(\text{ u}\)) \(\times\) (931.5 \(\text{ MeV/c}\)^2)

. This gives the total energy in MeV.

Step 4: Perform the multiplication to find the total energy in MeV. Multiply the given mass (0.185 u) by the conversion factor (931.5 MeV/u).

Step 5: Interpret the result. The calculated energy represents the total kinetic energy of the fission products in MeV. Ensure the units are consistent and the result is expressed in MeV.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

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

Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², states that mass can be converted into energy and vice versa. In nuclear reactions, such as fission, a small amount of mass is lost and converted into a significant amount of energy, which can be calculated using this relationship. This principle is fundamental for understanding how nuclear reactions release energy.

Fission Process

Fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts, typically producing two or more lighter nuclei, along with the release of energy and neutrons. In the given reaction, the fission of Uranium-235 (²³⁵U) leads to the formation of Barium (¹⁴⁴Ba) and Krypton (⁸⁹Kr), along with additional neutrons. This process is crucial for nuclear power generation and atomic bombs.

Kinetic Energy of Fission Products

The kinetic energy of fission products refers to the energy possessed by the fragments produced during the fission process. This energy arises from the conversion of the mass lost during the reaction into kinetic energy, which can be calculated using the mass-energy equivalence principle. The total kinetic energy can be expressed in units such as MeV (mega-electronvolts), which is commonly used in nuclear physics.

Recommended video:

Guided course

09:07

Introduction to Dot Product (Scalar Product)

Related Practice

Textbook Question

In one of Thomson’s experiments he placed a thin metal foil in the electron beam and measured its temperature rise. Consider a cathode-ray tube in which electrons are accelerated through a 2000 V potential difference, then strike a 10 mg copper foil. What is the electron-beam current if the foil temperature rises 6.0°C in 10 s? Assume no loss of energy by radiation or other means. The specific heat of copper is 385 J/kg K .

views

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?

views

Textbook Question

A ²²²Rn atom (radon) in a 0.75 T magnetic field undergoes radioactive decay, emitting an alpha particle in a direction perpendicular to $\vec{B}$ . The alpha particle begins cyclotron motion with a radius of 45 cm. With what energy, in MeV, was the alpha particle emitted?

views

rank

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

The oxygen nucleus ¹⁶O has a radius of 3.0 fm. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.

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.

views