Book edition 1st

Author(s) Daniel V. Schroeder

Pages 356 pages

ISBN 9780201380279

Answers without the blur.

Just sign up for free and you're in.

Short Answer

The first excited energy level of a hydrogen atom has an energy of 10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of $S = k \ln 4$ , since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative? (Comment: When F for the level is negative, the atom will spontaneously go from the ground state into that level, since F=0 for the ground state and F always tends to decrease. However, for a system this small, the conclusion is only a probabilistic statement; random fluctuations will be very significant.)

Helmholtz free energy is positive when temperature T < 8.5 x 10⁴K and it is negative when temperature T < 8.5 x 10⁴K .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Given Information

Entropy, $S = k \ln (4)$
Where value of $k = 8.62 \times 10^{- 5} {eVK}^{- 1}$ Helmholtz free energy, F=0 (For ground state)First excitation of energy level, $U = 10.2 eV$

Explanation

Helmholtz free energy of the first excited level is given by

$F = U - T S F = U - T [k \ln (4)]$

Substitute the given value and calculate

$F = U - T [k \ln (4)]$

Rearrange

$T = \frac{U - F}{k \ln (4)}$

Since, for a ground state F=0,
After substituting the given values in the above equation we get

$T = \frac{10.2 eV - 0}{(8.62 \times 10^{- 5} {eVK}^{- 1}) \ln (4)} = 8.5 \times 10^{4} K$

Find Study Materials for

Create Study Materials

Select your language

An Introduction to Thermal Physics

Answers without the blur.

Short Answer

Step by Step Solution

Given Information

Explanation

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

An Introduction to Thermal Physics

Answers without the blur.

Short Answer

Step by Step Solution

Given Information

Explanation

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

Famous Physicists

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