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

Question: Consider the fission of ${}^{238}U$ by fast neutrons. In one fission event, no neutrons are emitted and the final stable end products, after the beta decay of the primary fission fragments, are ${}^{140}C e and {}^{99}{Ru}$ . (a) What is the total of the beta-decay events in the two beta-decay chains? (b) Calculate for this fission process. The relevant atomic and particle masses are
${}^{238}U 238.05079 {}^{140}{Ce} 139.90543 u n 1.00866 u {}^{99}{Ru} 9890594 u$

(a) The number of the beta decay is 10.

(b) The energy release in fission process is 225.98Me V.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The mass of ${}^{238}U, m_{u} = 238.05079 u$

The mass of ${}^{140}C e, m_{C e} = 139.90543 u$

The mass of $n, m_{n} = 1.00866 u$

The mass of ${}^{99}R u, m_{R u} = 98.90594 u$

Step 2: Determine the formulas to calculate the number of the beta decay and energy for the fission process.

The expression to calculate released energy is given as follows.

$Q = - ∆ m c^{2} Q = (m_{u} + m_{n} - m_{C e} - m_{R u} - N m_{e}) c^{2}$ ...(i)

Here,N is the number of the beta decay.

Step 3: (a) Calculate the number of the beta decay.

Consider the reaction given below.

${}^{238}U + n \to {}^{140}C e + {}^{99}R u + N e$

Here, is the number of the beta decay.

To calculate the number of the beta decay, equals the atomic number of both the sides of the equation.

Atomic number of uranium, $Z_{u} = 92$

Atomic number of cerium, $Z_{C e} = 58$

Atomic number of Ruthenium, $Z_{R u} = 44$

Calculate the number of beta decay.

$N e + Z_{R u} + Z_{C e} = Z_{u}$

Substitute for 92 for $Z_{u}$ , 58 for $Z_{C e}$ , 44 for $Z_{R u}$ and 1 for e into above equation.

$N (1) + 44 + 58 = 92 N + 102 = 92 N = 92 - 102 N = - 10$

Here, negative sign indicates that beta decay reduces the atomic number.

Hence the number of the beta decay is 10.

Step 4: (b) Calculate the energy for the fission process.

Recall equation (i).

$Q = (m_{u} + m_{n} - m_{Ce} - m_{Ru} - {Nm}_{e}) \times c^{2} Q = (m_{u} + m_{n} - m_{Ce} - m_{Ru}) c^{2} - (m_{e} c^{2})$

Substitute f $238.05079 u for m_{u}$ , $139.90543 u for m_{Ce}$ , $1.00866 u for m_{n}$ , $98.90594 u for m_{Ru}$ , $931.5 MeV for c^{2}$ , $0.511 MeV for m_{e} c^{2}$ and 10 for N into equation (i).

role="math" localid="1661924965359" $Q = (238.05078 + 1.00866 - 139.90543 - 98.90594) 931.5 MeV - 10 \times 0.511 MeV Q = 0.24809 \times 931.5 MeV - 10 \times 0.511 MeV Q = 231.095835 MeV - 5.11 MeV Q = 225.99 MeV$

Hence the energy release in fission process is $225.99 MeV$ .

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: Determine the formulas to calculate the number of the beta decay and energy for the fission process.

Step 3: (a) Calculate the number of the beta decay.

Step 4: (b) Calculate the energy for the fission 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

Step by Step Solution

Step 1: Given data

Step 2: Determine the formulas to calculate the number of the beta decay and energy for the fission process.

Step 3: (a) Calculate the number of the beta decay.

Step 4: (b) Calculate the energy for the fission 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