If you agree to the license, it gives you certain privileges that you would not otherwise have, such as the right to copy the book or download the digital version for free from www.lightandmatter.com. 75 A wrong interpretation: photons interfering with each other, 76.—The concept of the path of a photon is undefined., 76.—.
Relativity
Time Is Not Absolute
The two traveling clocks had effects in opposite directions, suggesting that the speed at which time passes depends on the movement of the observer. The behavior of the three clocks in the Hafele-Keating experiment shows that the amount of time distortion increases as the speed of the clock increases.
Distortion of Space and Time
The slope shown in the figure gives the relative velocity of the two reference frames. Let's think a little more about the role of the 45-degree diagonal in the Lorentz transformation.
Dynamics
But at very high velocities, γ becomes very large - the small ball in Fig. x has a γ of 5.0 and therefore has five times more inertia than would be expected non-relativistically. The operation of the heater then does not affect the motion of the ship because the total energy in the ship remained unchanged; one form of energy (electricity) was simply converted into another (heat).
Summary
When an object is moving, the mass-energy excess, in addition to mc2, can be interpreted as its kinetic energy. This book explains that general relativity is neither fantasy nor scripture, but a scientific theory like any other.
Problems
In this homework problem, complete the algebra steps needed to find the equation for γ on page 20. Calculate the momentum of the recoil flashlight, in units of kg·m/s. f) Discuss how your answer in part e relates to the correspondence principle.
Rules of Randomness
- Randomness Isn’t Random
- Calculating Randomness
- Probability Distributions
- Exponential Decay and Half-Life
They make statements like, "The evolution of a complex organism like Homo sapiens by chance would be like a vortex blowing through the waste and spontaneously assembling a jumbo jet from scrap iron." The flaw in this type of reasoning is that it ignores the deterministic constraints on the outcomes of random processes. Here, I represent probabilities as numbers from 0 to 1, which is clearer than statements like "The odds are 999 to 1," and makes calculations easier. Argentine author Jorge Luis Borges wrote a short story called "The Library of Babel" in which he imagined a library containing all the books that could be written with the letters of the alphabet.
It also gives us a way to calculate the rate of decay, that is, the number of decays per unit time. A nuclear physicist with a demented sense of humor throws you a cigar box and shouts "hot potato". The label on the box says.
Applications of Calculus
The expected time until the sample completely decays depends on how much of the substance you have. If the original 238U atom is in solid rock (as opposed to Earth's molten regions), the He atoms are unable to diffuse out of the rock. Many heavy elements decay by alpha emission due to the strong electrical repulsion of all their protons.).
We measure the random distance r from the center of the circle to where the bullet entered. a) Show that the probability distribution of r must be of the form D(r) =kr, where is some constant. R 13 The speed, v, of an atom in an ideal gas has a probability distribution of the form D(v) =bve−cv2, where 0≤v <∞,corresponds to the temperature, and bis is determined by normalization . c) Find the average speed in terms of c, eliminating b.
Light as a Particle
- Evidence for Light As a Particle
- How Much Light Is One Photon?
- Wave-Particle Duality
- Photons In Three Dimensions
Max Planck began the photon saga with a theoretical study of the light spectrum emitted by a hot, glowing object. A The photoelectric effect ejects only a very small percentage of the available electrons near the surface of an object. The moral is that we should not think in terms of a photon.
More specifically, the probability distribution of the particle must be proportional to the square of the wave's amplitude. Around the turn of the twentieth century, experiments began to show problems with the classical wave theory of light.
Matter as a Wave
- Electrons As Waves
- Bound States
- The Uncertainty Principle
- Electrons In Electric Fields
It is more accurate to describe the electron as a wave that undergoes 100% reflection at the boundaries of the box. In quantum physics, these wave patterns are called "states" of the system of particles in the box. Although their standing wave models are not as simple as those of box particles, their energies are quantized.
The uncertainty in our knowledge of the electron's momentum is ∆p= 2h/λ, which covers the range between these two values. Schr¨odinger describes the wave function of the box's contents at the end of the hour:.
The Schr ¨ odinger Equation
In fact, this is a simplified version of the Schr¨odinger equation that applies only to standing waves in one dimension.). This leads us to a quantitative calculation of the tunneling effect, which is briefly discussed in the previous subsection. If we continue to believe in the equation KE = p2/2m, then the particle's momentum is apparently the square root of a negative number.
An electron in an atom typically has a speed of about 1% of the speed of light. a) Calculate the momentum of the electron. 7 If x has a mean value of zero, then the standard deviation of the probability distribution D(x) is defined by.
The Atom
Classifying States
Momentum is also a conserved quantity, but it is not very suitable for classifying the states of the electron in a hydrogen atom. There is no transfer of angular momentum between the proton and the electron, since the force between them is a center-to-center force that produces no torque. The larger this integer, the shorter the wavelength, and a shorter wavelength relates to greater momentum and angular momentum.
In the quantum moat example, angular momentum is quantized in units of h/2π, and this turns out to be a completely general fact about quantum physics. The angular momentum of a particle due to its motion through space is quantized in units of ~.
Angular Momentum In Three Dimensions
Three-Dimensional Angular Momentum in Quantum Physics When we begin to think more carefully about the role of angular momentum in quantum physics, it may appear that there is a fundamental problem: the angular momentum of the electron in a hydrogen atom depends on both its distance from the proton and its momentum, so that knowing its angular momentum precisely, it seems that we should know both its position and momentum simultaneously with good accuracy. Indeed, the uncertainty principle places limits on what can be known about a particle's angular momentum vector, but it does not prevent us from knowing its magnitude as an exact integer multiple of . We may not be able to know both x and px with unbounded accuracy, but we can still know the particle's angular momentum about the origin accurately.
It has angular momentumxpy about the zaxis, and again we can know its angular momentum with unbounded accuracy because the uncertainty principle on relatesx topx and y topy. However, it prevents us from knowing all three components of an angular momentum vector simultaneously.
The Hydrogen Atom
A The quantum number is defined as the number of radii at which the wave function is zero, including r. C Relate the features of the wave function graphs in figure f to the corresponding features of the probability distribution plots. D How can you tell from the wave function graphs in figure f which one has which angular momenta.
E Criticize the following incorrect statement: "The wave function i`= 8 in figure d has a shorter wavelength in the center because in the center the electron is in a higher energy level.". F Discuss the implications of the fact that the probability cloud in the state n= 2,`= 1 splits into two parts.
5.4 ? Energies of States In Hydrogen
Electron Spin
Experiments show that even when an electron is not moving through space, it still has an angular momentum of ~/2. However, that entire discussion assumed that the angular momentum would come from the motion of a particle through space. The ~/2 angular momentum of the electron is simply a property of the particle, like its charge or its mass.
The symbols `and`z include only the angular momentum the electron has as it moves through space, not the spin angular momentum. The availability of two possible electron spin states leads to a doubling of the number of states:
Atoms With More Than One Electron
4 Find an equation for the wavelength of the photon emitted when the electron in a hydrogen atom makes a transition from energy level 1 to level 2. 7 The wave function of the electron in the ground state of a hydrogen atom is a) Calculate symbolically, without inserting numbers, the probability that at any time the electron is inside the proton. How would the size of a muonic hydrogen atom in its ground state compare to the size of the normal atom.
10 Consider the classical model of the hydrogen atom in which the electron orbits the proton in a circle at constant speed. But there are also other contributions arising from the intrinsic spins of the electron and proton.].
Proofs
Proof that the Lorentz transformation preserves area
Interpretation of the equal-area property
Exercises
Exercise 1A: Sports in Slowlightland
Exercise 5A: Quantum Versus Classical Randomness
Photo Credits
Except as specifically noted below or in parentheses in the image title, all illustrations in this book are copyrighted by me and are copyrighted under the same license as the rest of the book. I have included some public domain images; their photographic reproductions are not protected by copyright in the United States. When "PSSC Physics" is credited, it means that the image is from the first edition of the Physics textbook published by the Physical Science Study Committee.
The early editions of these books never had their copyrights renewed, and are therefore now in the public domain. Credits to Millikan and Gale refer to the textbooks Practical Physics (1920) and Elements of Physics (1927). (the 1927 version did not have its copyright renewed.) Since it is possible that some of the illustrations in the 1927 version had their copyright renewed and are still under copyright, I have used them only when it was clear that they were originally taken from public domain sources.
Hints and Solutions
Answers to Self-Checks
The equation KE = p2/2m is non-relativistic, so it cannot be applied to an electron moving at relativistic speeds. Page 105, self-check E: Dividing by Planck's constant, a small number, gives a large negative result inside the exponential, so the probability will be very small. Page 113, self-check A: If you trace a circle going around the center, you run into a series of eight complete wavelengths.
Index
Useful Data
Metric Prefixes
The Greek Alphabet
Subatomic Particles
Notation and Units
Earth, Moon, and Sun
Fundamental Constants
