Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A $^{238} \cup$ nucleus emits an 4.196 MeV alpha particle. Calculate the disintegration energy Q for this process, taking the recoil energy of the residual $^{238} T h$ nucleus into account.

The disintegration energy for the process of a uranium nucleus emitting an alpha particle is 4.269 MeV.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Energy of the alpha particle, $E_{α} = 4.196 M e V$

Step 2: Understanding the concept of decay

The disintegration energy, also known as the Q-value, is the energy that is absorbed or released when a nuclear reaction takes place. The recoiling energy of the thorium is the translational energy of the thorium nucleus. Considering the energy and momentum conservation concept, we can get the value of this recoiling energy. Again, the total energy released by the alpha particle and thorium will give the disintegration energy.

Formula:

The kinetic energy of the particle according to classical concept, $K = \frac{p^{2}}{2 m}$ (i)

Step 3: Calculation of the disintegration energy of the process

Energy and momentum are conserved. We assume the residual thorium nucleus is in its ground state.

Let, $K_{α}$ be the kinetic energy of the alpha particle and $K_{T h}$ be the kinetic energy of the thorium nucleus. Then, the disintegration energy for the process emitting the alpha particle and thorium nuclide is given as:

$Q = K_{α} + K_{T h} . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)$

We assume the uranium nucleus is initially at rest. Then, conservation of momentum yields

$\begin{array}{l} 0 = p_{α} + p_{T h} \\ p_{T h} = - p_{α} \dots \dots \dots . . . . \dots \dots \dots (b) \end{array}$

Where, $p_{α}$ is the momentum of the alpha particle and $p_{T h}$ is the momentum of the thorium nucleus.

Both particles travel slowly enough that the classical relationship between momentum and energy can be used.

Thus, using equation (i), the kinetic energy of the thorium nucleus is given as:

$K_{T h} = \frac{p_{T h}}{2 m_{T h}}$

Now, using the value of momentum from equation (a) and using the kinetic energy value from equation (i), we get the above value as:

$K_{T h} = \frac{P_{α}^{2}}{2 m_{T h}} = \frac{m_{α}}{m_{T h}} K_{α}$

Now, using the above value in equation (a), we can get the disintegration energy as follows:

$Q = K_{α} + \frac{m_{α}}{m_{T h}} K_{α} = 4.196 M e V + (\frac{4 u}{234 u}) (4.196 M e V) = 4.196 M e V + 0.07313 M e V \approx 4.269 M e V$

Hence, the value of the disintegration energy is $4.269 M e V$ .

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

A $^{238} \cup$ nucleus emits an 4.196 MeV alpha particle. Calculate the disintegration energy Q for this process, taking the recoil energy of the residual $^{238} T h$ nucleus into account.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of decay

Step 3: Calculation of the disintegration energy of the process

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

A 238∪ nucleus emits an 4.196 MeV alpha particle. Calculate the disintegration energy Q for this process, taking the recoil energy of the residual 238Th nucleus into account.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of decay

Step 3: Calculation of the disintegration energy of the process

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

A $^{238} \cup$ nucleus emits an 4.196 MeV alpha particle. Calculate the disintegration energy Q for this process, taking the recoil energy of the residual $^{238} T h$ nucleus into account.