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

What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap $E_{g} (= 5.5 eV)$ in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.

The probability that an electron will jump across the energy gap in a diamond is $1.28 \times 10^{- 42}$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

a) Temperature of the energy state, T = 300 K

b) Value of energy gap, $E_{g} = 5.5 eV$

c) Mass of Earth, $M_{e} = 5.98 \times 10^{24} kg$

d) Molar mass of carbon, m = 12.01 g/ mol

e) Assumption that in diamond there is one valence electron per carbon atom

Step 2: Understanding the concept of Fermi energy

The highest energy level occupied by an electron in the valence band at absolute zero temperature is known as Fermi level and the energy of electrons present in that level is known as Fermi energy.

Formulae:

Number of excited atoms in a mass,

$N_{e} = \frac{M_{e}}{m} N_{A}$ (i)

$where N_{A} = 6.02 \times 10^{23}$ is called Avogadro’s number.

The probability of an electron to get excited in an insulator,

$P = N_{e}^{- E_{g} / k T}$ (ii)

$where k = 8.62 \times 10^{- 5} eV$

Step 3: Calculation of the probability of excitation atoms to jump an given energy band gap

The number of carbon atoms in a diamond, as massive as the Earth, is given by the number of electrons that get excited.

Thus, using equation (i) and equation (ii), the probability for an electron to get excited is given as-

$P = (\frac{M_{e}}{m} N_{A}) e^{(- E_{g} / k T)} = (\frac{(5.98 \times 10^{24} kg) (6.02 \times 10^{23} / mol)}{12.01 g / mol}) e^{(\frac{- 5.5 eV}{(8.62 \times 10^{- 5} eV / K) 300 K})} = 1.28 \times 10^{- 42}$

Hence, the value of the probability is $1.28 \times 10^{- 42}$ .

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap $E_{g} (= 5.5 eV)$ in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of Fermi energy

Step 3: Calculation of the probability of excitation atoms to jump an given energy band gap

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

What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap Eg(=5.5 eV) in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of Fermi energy

Step 3: Calculation of the probability of excitation atoms to jump an given energy band gap

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

What is the probability that, at a temperature of T = 300 K, an electron will jump across the energy gap $E_{g} (= 5.5 eV)$ in a diamond that has a mass equal to the mass of Earth? Use the molar mass of carbon in Appendix F; assume that in diamond there is one valence electron per carbon atom.