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

Large radionuclides emit an alpha particle rather than other combinations of nucleons because the alpha particle has such a stable, tightly bound structure. To confirm this statement, calculate the disintegration energies for these hypothetical decay processes and discuss the meaning of your findings:
$(a) {}^{238}U \to {}^{232}{Th} + {}^{3}{He} (b) {}^{235}U \to {}^{231}{Th} + {}^{4}{He} (c) {}^{235}U \to {}^{230}{Th} + {}^{5}{He}$
The needed atomic masses are
role="math" localid="1661928659878" ${}^{232}{Th} 232.0381 u {}^{3}{He} 3.0160 u {}^{231}{Th} 231.0363 u {}^{4}{He} 4.0026 u {}^{230}{Th} 230.0331 u {}^{5}{He} 5.0122 u {}^{235}U 235.0429 u$

The disintegration energy for the hypothetical decay ${}^{235}U \to {}^{232}{Th} + {}^{3}{He}$ is - 9.50 MeV.
The disintegration energy for the hypothetical decay ${}^{235}U \to {}^{231}{Th} + {}^{4}{He}$ is 4.66 MeV.
The disintegration energy for the hypothetical decay ${}^{235}U \to {}^{230}{Th} + {}^{5}{He}$ is - 1.30 MeV.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The given atomic masses of the nuclides and alpha particles are:

${}^{232}{Th} 232.0381 u {}^{3}{He} 3.0160 u {}^{231}{Th} 231.0363 u {}^{4}{He} 4.0026 u {}^{230}{Th} 230.0331 u {}^{5}{He} 5.0122 u {}^{235}U 235.0429 u$

Step 2: Understanding the concept of decay

Massive nuclides tend to undergo alpha decay releasing disintegration energy. The disintegration energy, also known as the Q-value, is the energy that is absorbed or released when a nuclear reaction takes place. The Q-value is positive if the reaction is exothermic and negative if the reaction is endothermic. The potential barrier height of the nucleus indicates the energy it needs to overcome the internal forces and become an individual nucleus from the parent nucleus.

Formula:

The disintegration energy of a nuclear reaction,

$Q = (m_{p a r e n t n u c l e u s} - (\sum_{} m_{d a u g h t e r n u c l e i})) c^{2}$ …… (i)

Step 3: a) Calculate the disintegration energy

The disintegration energy for uranium-235 “decaying” into thorium-232 is given using the atomic masses and equation (i) as follows:

$Q = (m_{235_{U}} - m_{232_{Th}} - m_{3_{He}}) c^{2}$

Substitute the values and solve as:

$Q = (235.0429 u - 232.0381 u - 3.0160 u) (931.5 \frac{M e V}{u}) = - 9.50 M e V$

Hence, the disintegration energy is - 9.50 MeV.

Step 4: b) Calculate the disintegration energy

The disintegration energy for uranium-235 decaying into thorium-231 is given using the atomic masses and equation (i) as follows:

$Q = (m_{235_{U}} - m_{231_{Th}} - m_{4_{He}}) c^{2}$

Substitute the values and solve as:

$Q = (235.0429 u - 231.0363 u - 4.0026 u) (931.5 \frac{M e V}{u}) = 4.66 M e V$

Hence, the disintegration energy is 4.66 MeV.

Step 5: c) Calculate the disintegration energy

The disintegration energy for uranium-235 decaying into thorium-230 is given using the atomic masses and equation (i) as follows:

$Q = (m_{235_{U}} - m_{230_{Th}} - m_{5_{He}}) c^{2}$

Substitute the values and solve as:

role="math" localid="1661929289112" $Q = (235.0429 u - 230.0331 u - 5.0122 u) (931.5 \frac{M e V}{u}) = - 1.30 M e V$

Hence, the disintegration energy is - 1.30 MeV.

Only the second decay process (the $α$ decay) is spontaneous, as it releases energy considering the positive sign of Q-value.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept of decay

Step 3: a) Calculate the disintegration energy

Step 4: b) Calculate the disintegration energy

Step 5: c) Calculate the disintegration energy

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

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept of decay

Step 3: a) Calculate the disintegration energy

Step 4: b) Calculate the disintegration energy

Step 5: c) Calculate the disintegration energy

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