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 hypothetical atom has only two atomic energy levels, separated by 32 eV . Suppose that at a certain altitude in the atmosphere of a star there are $6.1 \times 10^{13} / {cm}^{3}$ of these atoms in the higher-energy state and $2.5 \times 10^{15} / {cm}^{3}$ in the lower-energy state. What is the temperature of the star’s atmosphere at that altitude?

The temperature of the star’s atmosphere at that altitude is $1 \times 10^{4} K$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The energy difference between two atomic levels of an atom, $∆ E = 3.2 eV$

Number of atoms in the higher-energy state, $N_{1} = 6.1 \times 10^{13} / {cm}^{3}$

Number of atoms in the lower-energy state, $N_{2} = 2.5 \times 10^{15} / {cm}^{3}$

Step 2: Understanding the concept of the Boltzmann distribution equation:

The Boltzmann distribution is a probability function used in statistical physics to define the state of a particle system in terms of temperature and energy.

Using the Boltzmann-distribution equation which is the expression for the probability for stimulated emission of radiation to the probability for spontaneous emission of radiation under thermal equilibrium defines the temperature of the star at that altitude using the given data in the probability equation.

Formula:

The Boltzmann energy distribution equation,

$\frac{N_{1}}{N_{2}} = e^{- (E_{2} - E_{1}) / kT}$ ….. (1)

Here, a constant, $k = 1.38 \times 10^{- 23} J / K$

Step 3: Calculation of the temperature of the star’s atmosphere

Using the given data in equation (1), the temperature of the star’s atmosphere at that altitude is as follow.

$T = \frac{E_{2} - E_{1}}{kIn (N_{2} / N_{1})}$

Substitute known values in the above equation.

$T = \frac{3.2 eV}{(1.38 \times 10^{- 23}) In (2.5 \times 10^{15} / 6.1 \times 10^{13})} = 1 \times 10^{4} K$

Hence, the value of the temperature is $1 \times 10^{4} K$ .

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: The given data

Step 2: Understanding the concept of the Boltzmann distribution equation:

Step 3: Calculation of the temperature of the star’s atmosphere

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: The given data

Step 2: Understanding the concept of the Boltzmann distribution equation:

Step 3: Calculation of the temperature of the star’s atmosphere

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