Bahan Ajar Fisika Modern PGMIPA-BI (sebagian)

Teaching Material

MODERN PHYSICS

1.

Einstein’s Theory of Special Relativity

2.

Quantum Phenomenon

3.

Quantum Theory of Light

4.

Atom Models

5.

The Compton Effect

6.

Blackbody Radiation

7.

Matter Waves

8.

The Uncertainty Principle of Heisenberg

9.

Radioactivity

By:

Imelda Paulina Soko, M.Pd

PHYSICS EDUCATION STUDY PROGRAMME

MATHEMATICS AND NATURAL SCIENCE EDUCATION

DEPARTMENT

FACULTY OF TEACHER TRAINING AND EDUCATIONAL SCIENCES

UNIVERSITY OF NUSA CENDANA

2013

We declare that this particular material entitled Modern Physics is our original work and has never been funded by other sources accordance based on the standard of writing a modular teaching materials for a lecturer in Nusa Cendana University.

If it turns out later that this statement is not true, then we are willing to account for it.

Kupang, December 2012 Writer

APPROVAL

Tittle : Modern Physics

Writers : Drs. Fakhruddin, M.Si and Imelda Paulina Soko, M.Pd Has been examined carefully that the modul is original and fits the standard of writing a modular teaching materials for a lecturer in Nusa Cendana University.

PREFACE

This teaching material is expected can support the achievement of the learning aims of Modern Physics one semester courses. The material which is developed in this teaching material is the material of elementary classical physics and calculus as prerequisites. Relativity and quantum theory are considered first to provide a framework for understanding the physics of atoms and nuclei.

We are grateful to all for the helpful suggestions and support in this regard. Your insights will help enhance this collection of teaching materials and along the way will educate more of our youth about Modern Physics.

Kupang, December 2012

Writer

1. Name of course : Modern Physics 2. Code of course : KPE 4517

3. Credit : 4

4. Status of course : Compulsory Course Description:

This course is a compulsory course for the students of physics study program which is taught to the students of the 5th _{semester in}

bachelor degree. This course deals with many basic understandings and information of Modern Physics such as theory of relativity, quantum physics, statistic physics, and nuclear physics. This course explores the foundations of Einstein’s Theory of Special Relativity and its applications to our understanding of nuclear and particle physics. The history of the development of our conceptual understanding of space and time, and the pedagogical issues that arise in teaching this material, are addressed.

TABLE OF CONTENTS

Tittle...i

Statement of Authorship...ii

Approval...iii

Preface...iv

Course Identity...v

Table of Contents...vi

1. Einstein’s Theory of Special Relativity...1

2. Quantum Phenomenon...18

3. Quantum Theory of Light...28

4. Atom Models...34

5. The Compton Effect...47

6. Blackbody Radiation...52

7. Matter Waves...58

8. The Uncertainty Principle of Heisenberg...67

9. Radioactivity...73

BIBLIOGRAPHY...82

1. A photon and a particle have the same wavelength. (a) Compare their linear momentum, (b) Compare the photon's energy and the particle's total energy. (c) Compare the photon's energy and the particle's kinetic energy.

2. Show that the Broglie wavelength of a particle of rest mass mo and

kinetic energy K is _{K(K 2m c}2

hc

o

 

 _!

2.

Quantum Phenomenon

lines of hydrogen), the electrons are always found at certain distinct distances from the nucleus?

2. Why is the wave nature of matter not more apparent to us in our everyday lives?

3.

Quantum Theory of Light

1.

The work function of potassium is 2,2 eV. When ultraviolet light of wavelength 3500 Å (1 Å=10-10 _{m) falls on potassium surface,}

what is the maximum energy in electron volts of photoelectrons?

2.

How much energy must a photon have if it is lo have the momentum of a 10 MeV proton?

3.

What is the frequency of an X-ray photon whose momentum is 1,1 X lO-23 _kg.m/s?

4.

Atom Models

Exercise:

1. Explain why Rutherford is quoted as saying, “It was quite the most incredible event that has ever happened to me in my life. It was

and the current model of the atom to explain why Geiger and Marsden saw what they saw.

2. What were Bohr’s four assumptions?

Exercise:

1. An x-ray photon is scattered by an electron. The frequency of the scattered photon relative to that of the incident photon (a) increases, (b) decreases, or (c) remains the same.

2. The distance between adjacent atomic planes in calcite is 3x108

cm. What is the smallest angle between these planes and an incident beam of 0.3 Å x-rays at which scattered x-rays can be detected?

3. A beam of x-rays is scattered by free electrons. At 450 _{from the}

beam direction the scattered x-rays have a wavelength of 0.022 Å. What is the wavelength of the x-rays in the direct beam?

6.

Blackbody Radiation

this microwave radiation?

2. Calculate the energies of one photon of ultraviolet ( = 1x10-8

7.

Matter Waves

Exercise:

1. Derive a formula for the de Broglie wavelength of a particle in terms of its kinetic energy T and its rest energy m0c2, how does the

particle’s wavelength compare with the wavelength of a photon of the same energy?

2. Assume that electromagnetic waves are a special case of de Broglie waves. Show that photons must travel with the velocity c and that the rest mass of the photon must be 0!

3. Obtain the de Broglie wavelength of a moving particle in the following way, which parallels de Broglie’s original treatment. Consider a particle of rest mass m0 as having a characteristic

frequency of vibration of p0 specified by the relationship hv0 = m0

c2

. The particle travels with the speed v realtive to an observer.

With the help of special relativity, show that the observer sees a progressive wave whose phase velocity is

 

2

c

 and whose

wavelength is mc h , where 2 2 0 1 c v m m   . 4. The velocity of ocean waves is

  2

g

, where g is the acceleration of gravity. Find the group velocity of these waves!

5. The velocity of ripples on a liquid surface is

  2

, where S is the surface tension and  the density of the liquid. Find the group group velocity of these waves!

Exercise:

1. The position and momentum of a 1 keV electron are simultaneously determined. If its position is located to within 1 Å, what is the percentage of uncertainty in its momentum?

2. An electron microscope uses 40 keV electrons. Find its ultimate resolving power on the assumption that this is equal to the wavelength of the electrons!

3. Compare the unertainties in the velocities of an electron and a proton confined in a 10 Å box!

4. Wavelengths can be determined with accuracies of one part in 106_.

What is the uncertainty in the position of a 1 Å x-ray photon when its wavelength is simultaneously measured?

Exercise:

1. Tritium

 

3H

1 has a half life of 12,5 year against beta decay. What

fraction of a sample of pure tritium will remain undecayed after 25 year?

2. The half life of



24Na



11 is 15 hours. How long does it take for

93,75% of a sample of this isotope to decay?

3. 1 g of radium has an activity of 1 Ci. From this fact determine the half life of radium!

BIBLIOGRAPHY

Beiser, Arthur. 1973. “Concepts of Modern Physics", Second Edition. McGraw-Hill, Japan.

Betle , A. Hans , Jackiw, W. Roman. 1985. "Intermediate Quantum Mechanics ", Third Edition. Addison-Wesley Publising Company, Corolado.

Hans H. H, Wolf Christoph. 1996. "The Physics of Atoms and Quanta", Fifth Edition. Universitat Stuttgart, Stuttgart.

Exercise:

1. Tritium

 

3H

1 has a half life of 12,5 year against beta decay. What

fraction of a sample of pure tritium will remain undecayed after 25 year?

2. The half life of



24Na



11 is 15 hours. How long does it take for

93,75% of a sample of this isotope to decay?

3. 1 g of radium has an activity of 1 Ci. From this fact determine the half life of radium!

BIBLIOGRAPHY

Beiser, Arthur. 1973. “Concepts of Modern Physics", Second Edition. McGraw-Hill, Japan.

Betle , A. Hans , Jackiw, W. Roman. 1985. "Intermediate Quantum Mechanics ", Third Edition. Addison-Wesley Publising Company, Corolado.

Hans H. H, Wolf Christoph. 1996. "The Physics of Atoms and Quanta", Fifth Edition. Universitat Stuttgart, Stuttgart.