Thursday, October 11, 2007
Quantum Mechanics
MAX PLANCK AND HIS QUANTUM THEORY
There is a nice balance in the respective theories which Professor Max Planck and Professor Einstein put forward. Whereas Professor Einstein taught the relativity of physical measurements which formerly had been thought to have absolute significance, Planck discovered in nature an absolute unit where previously relativity had held sway. This unit is known as the quantum of action. It has the dimensions of energy multiplied by time, and is exceedingly minute, being about 6.55 × 10-27 erg-seconds. Nevertheless it is the most fundamental constant in nature. Planck first put forward his theory to account for certain phenomena in the study of heat radiation, but it has subsequently been found applicable to all phenomena on an atomic scale where observation is sufficiently close to make a test possible. His theory may now be put forward as a general law of nature, that energy is not liberated continuously by atoms or molecules, but discretely, in quanta or “packets.” The theory can be expressed in a simple formula—and Planck firmly believed throughout his life that the more general the law the simpler its expression. If ε is the energy transmitted as a vibration of frequency v there is a constant h (Planck’s constant) such that ε/v is h, or 2h, or some other small integral multiple of h. This discovery of a fundamental discontinuity in the processes of nature can hardly be underestimated. It is parallel to the discontinuity in matter revealed by the discovery of the electron and proton. Since the introduction of the infinitesimal calculus by Leibniz and Newton, physics had been built on the assumption of the continuity of all causal chains of events. The discovery of a universal quantum of action has upset this basis; and for the discovery Plank bears the undivided glory.
Max Planck was born at Kiel on April 23, 1858. His father, who was Professor of Constitutional Law at Kiel University, and later at Göttingen, was joint author of the Prussian Civil Code. Planck’s faculty for sifting experimental evidence has sometimes been attributed to his parentage, but as this faculty has been a sine qua non of all great men of science, irrespective of parents, it need not be ascribed to heredity. At the age of 17 he entered Munich University, where his main subject was physics. Three years later he attended courses at Berlin University and sat at the feet of that great triumvirate, Helmholtz, Kirchhoff, and Weierstrass. It was Kirchhoff who directed his attention to thermodynamics. His thesis for the doctorate, which he received from the University of Munich summa cum laude in 1879, was on the Second Law of Thermodynamics. After five years as a Privatdozent at Munich, Planck was appointed Professor of Physics at the University of his native town. In 1889 he left Kiel for Berlin as Professor Extraordinarius, and in 1892 succeeded Kirchhoff in the chair of Experimental Physics. There he remained for the rest of his teaching life.
Planck’s great discovery was announced in a paper “On the Distribution of Energy in a Normal Spectrum” communicated to the German Physical Society on December 14, 1900; it symbolized the end not only of a century but of an age. All the previous 20 years of his academic life had led in one way or another to this result, but Planck himself, on looking back at the “long and tortuous road,” was forcibly reminded of Goethe’s saying, Es irrt der Mensch so lang’ er strebt. Kirchhoff had shown that the distribution in wave-length of the heat radiation produced in an enclosure surrounded by any emitting or absorbing bodies, all at the same temperature, was independent of the nature of such bodies. This pointed to the existence of a universal function expressing the distribution of radiant energy in an enclosure in terms of temperature and wave-length, and Planck spent many years searching for this function. He met with many setbacks, but in 1899, when he attacked the problem from the standpoint of thermodynamics, success drew nearer. He was helped by the law enunciated in 1896 by Wien. His eventual discovery was the result of theoretical considerations based on the work of Boltzmann, and of a detailed study of the experimental results, particularly the then recent ones of Lummer and Pringsheim, on the distribution of energy in the spectrum of heat radiation from an enclosure. What he found was that the experimental results could only be expressed by assuming that the emission of radiant energy took place in discrete units, or quanta, the magnitude of which depended upon the frequency in question. To develop the subsequent history of the theory would be to re-tell one half of modern physics. It must suffice to indicate the main steps by which Planck’s discovery was elevated into a universal law of nature. They are Einstein’s law of the photoelectric effect (1905), which extended the principle to cover the transfer of energy from light to electrons; the close agreement of Planck’s deduction of the electronic charge with the measurements of Rutherford and Geiger (1908), which brought wide conviction of its truth; Bohr’s quantum theory of spectra (1913), with its derivation of Balmer’s formula and Rydberg’s constant; and Sommerfeld’s spectroscopic theories. In still more recent years the mathematical theories developed by de Broglie, Schrödinger, Heisenberg, and Dirac have crowned the work begun by Planck.
In 1907 Planck received an invitation to succeed Boltzmann as Professor of Physics at Vienna, but, while he felt honoured by the invitation, he decided to stay in Berlin. In 1912 he was appointed Permanent Secretary to the Prussian Academy for Science, and in the year 1913-14 was Rector of Berlin University. The Nobel Prize for Physics was awarded to him in 1918. In 1926 he became Professor Emeritus, Dr. Schrödinger succeeding him in the chair. He was elected a Foreign Member of the Royal Society in 1926, and in 1929 was awarded the society’s most coveted distinction, the Copley Medal. When Adolf Harnack died in 1930 it was almost inevitable that Planck should succeed him as president of the Kaiser Wilhelm Society, the highest academic post in Germany. Planck remained active long after the allotted span—he climbed the Jungfrau to celebrate his seventy-second birthday—and his position as the doyen of international science was undisputed, his house in the Grunewald colony being a Mecca for physicists the world over. His scientific writings, beginning as far back as 1879, dealt mainly with the subject of heat, but included lucid expositions of general physics, and showed that apart from his discovery of the quantum of action he would have been in the front rank of men of science.
He was also drawn into some discussion of the more philosophical aspects of science. Some years ago, in a discussion with Mach, he controverted the positivist theory which would reduce science to mere description. More recently he felt obliged to take notice of the sweeping philosophical deductions which were drawn from the quantum theory. It was commonly asserted that the old determinism of science had been banished and something approaching free will established in natural processes. Planck protested that for his part he believed the causal principle would be rehabilitated, though its traditional formulation might have to be revised. He even appeared to suggest that man’s consciousness of free will was an illusion, which would disappear on a fuller view, thus seemingly reversing Kant’s dictum about man’s empirical determinism and transcendental freedom.
Planck was held by his colleagues in a respect amounting to reverence. This was the result of extraordinary personal qualities no less than admiration for his scientific eminence. He united two seemingly opposed sets of characteristics, applying himself to routine questions with the most thorough patience and discipline and yet approaching major scientific problems in a profoundly original way. He showed in a supreme degree that greatest of scientific gifts, the disciplined imagination. He was an artist no less than a man of science, and it is worth recalling that at one time a musical career was seriously considered for him. In his work there was also something approaching a religious spirit. He decried scepticism, and insisted on the need for faith in the man of science. Professor Einstein once likened him to the devotee or lover, whose inspiration rose from a hunger of the soul.
He was twice married—in 1887 and 1911. By his first wife, Marie Merck, he had two sons and twin daughters, and by his second wife, Margaret von Hoesslin, another son. His domestic life was afflicted by sorrows which undoubtedly left their mark in his brooding countenance. His two daughters died soon after marriage, while a talented son lost his life in the war. Another son was wounded, but lived to become Secretary of State to the Chancellor in the von Papen Government.
With his wife he visited England in 1946, on the occasion of the Royal Society Newton celebrations, and they were obviously much gratified by the respectful attention shown to them by England’s leading men of science. Although physically feeble, the great man showed on that occasion a lively interest in all that was going on, and spoke with clear memory and affection of his former visits to England.
There is a nice balance in the respective theories which Professor Max Planck and Professor Einstein put forward. Whereas Professor Einstein taught the relativity of physical measurements which formerly had been thought to have absolute significance, Planck discovered in nature an absolute unit where previously relativity had held sway. This unit is known as the quantum of action. It has the dimensions of energy multiplied by time, and is exceedingly minute, being about 6.55 × 10-27 erg-seconds. Nevertheless it is the most fundamental constant in nature. Planck first put forward his theory to account for certain phenomena in the study of heat radiation, but it has subsequently been found applicable to all phenomena on an atomic scale where observation is sufficiently close to make a test possible. His theory may now be put forward as a general law of nature, that energy is not liberated continuously by atoms or molecules, but discretely, in quanta or “packets.” The theory can be expressed in a simple formula—and Planck firmly believed throughout his life that the more general the law the simpler its expression. If ε is the energy transmitted as a vibration of frequency v there is a constant h (Planck’s constant) such that ε/v is h, or 2h, or some other small integral multiple of h. This discovery of a fundamental discontinuity in the processes of nature can hardly be underestimated. It is parallel to the discontinuity in matter revealed by the discovery of the electron and proton. Since the introduction of the infinitesimal calculus by Leibniz and Newton, physics had been built on the assumption of the continuity of all causal chains of events. The discovery of a universal quantum of action has upset this basis; and for the discovery Plank bears the undivided glory.
Max Planck was born at Kiel on April 23, 1858. His father, who was Professor of Constitutional Law at Kiel University, and later at Göttingen, was joint author of the Prussian Civil Code. Planck’s faculty for sifting experimental evidence has sometimes been attributed to his parentage, but as this faculty has been a sine qua non of all great men of science, irrespective of parents, it need not be ascribed to heredity. At the age of 17 he entered Munich University, where his main subject was physics. Three years later he attended courses at Berlin University and sat at the feet of that great triumvirate, Helmholtz, Kirchhoff, and Weierstrass. It was Kirchhoff who directed his attention to thermodynamics. His thesis for the doctorate, which he received from the University of Munich summa cum laude in 1879, was on the Second Law of Thermodynamics. After five years as a Privatdozent at Munich, Planck was appointed Professor of Physics at the University of his native town. In 1889 he left Kiel for Berlin as Professor Extraordinarius, and in 1892 succeeded Kirchhoff in the chair of Experimental Physics. There he remained for the rest of his teaching life.
Planck’s great discovery was announced in a paper “On the Distribution of Energy in a Normal Spectrum” communicated to the German Physical Society on December 14, 1900; it symbolized the end not only of a century but of an age. All the previous 20 years of his academic life had led in one way or another to this result, but Planck himself, on looking back at the “long and tortuous road,” was forcibly reminded of Goethe’s saying, Es irrt der Mensch so lang’ er strebt. Kirchhoff had shown that the distribution in wave-length of the heat radiation produced in an enclosure surrounded by any emitting or absorbing bodies, all at the same temperature, was independent of the nature of such bodies. This pointed to the existence of a universal function expressing the distribution of radiant energy in an enclosure in terms of temperature and wave-length, and Planck spent many years searching for this function. He met with many setbacks, but in 1899, when he attacked the problem from the standpoint of thermodynamics, success drew nearer. He was helped by the law enunciated in 1896 by Wien. His eventual discovery was the result of theoretical considerations based on the work of Boltzmann, and of a detailed study of the experimental results, particularly the then recent ones of Lummer and Pringsheim, on the distribution of energy in the spectrum of heat radiation from an enclosure. What he found was that the experimental results could only be expressed by assuming that the emission of radiant energy took place in discrete units, or quanta, the magnitude of which depended upon the frequency in question. To develop the subsequent history of the theory would be to re-tell one half of modern physics. It must suffice to indicate the main steps by which Planck’s discovery was elevated into a universal law of nature. They are Einstein’s law of the photoelectric effect (1905), which extended the principle to cover the transfer of energy from light to electrons; the close agreement of Planck’s deduction of the electronic charge with the measurements of Rutherford and Geiger (1908), which brought wide conviction of its truth; Bohr’s quantum theory of spectra (1913), with its derivation of Balmer’s formula and Rydberg’s constant; and Sommerfeld’s spectroscopic theories. In still more recent years the mathematical theories developed by de Broglie, Schrödinger, Heisenberg, and Dirac have crowned the work begun by Planck.
In 1907 Planck received an invitation to succeed Boltzmann as Professor of Physics at Vienna, but, while he felt honoured by the invitation, he decided to stay in Berlin. In 1912 he was appointed Permanent Secretary to the Prussian Academy for Science, and in the year 1913-14 was Rector of Berlin University. The Nobel Prize for Physics was awarded to him in 1918. In 1926 he became Professor Emeritus, Dr. Schrödinger succeeding him in the chair. He was elected a Foreign Member of the Royal Society in 1926, and in 1929 was awarded the society’s most coveted distinction, the Copley Medal. When Adolf Harnack died in 1930 it was almost inevitable that Planck should succeed him as president of the Kaiser Wilhelm Society, the highest academic post in Germany. Planck remained active long after the allotted span—he climbed the Jungfrau to celebrate his seventy-second birthday—and his position as the doyen of international science was undisputed, his house in the Grunewald colony being a Mecca for physicists the world over. His scientific writings, beginning as far back as 1879, dealt mainly with the subject of heat, but included lucid expositions of general physics, and showed that apart from his discovery of the quantum of action he would have been in the front rank of men of science.
He was also drawn into some discussion of the more philosophical aspects of science. Some years ago, in a discussion with Mach, he controverted the positivist theory which would reduce science to mere description. More recently he felt obliged to take notice of the sweeping philosophical deductions which were drawn from the quantum theory. It was commonly asserted that the old determinism of science had been banished and something approaching free will established in natural processes. Planck protested that for his part he believed the causal principle would be rehabilitated, though its traditional formulation might have to be revised. He even appeared to suggest that man’s consciousness of free will was an illusion, which would disappear on a fuller view, thus seemingly reversing Kant’s dictum about man’s empirical determinism and transcendental freedom.
Planck was held by his colleagues in a respect amounting to reverence. This was the result of extraordinary personal qualities no less than admiration for his scientific eminence. He united two seemingly opposed sets of characteristics, applying himself to routine questions with the most thorough patience and discipline and yet approaching major scientific problems in a profoundly original way. He showed in a supreme degree that greatest of scientific gifts, the disciplined imagination. He was an artist no less than a man of science, and it is worth recalling that at one time a musical career was seriously considered for him. In his work there was also something approaching a religious spirit. He decried scepticism, and insisted on the need for faith in the man of science. Professor Einstein once likened him to the devotee or lover, whose inspiration rose from a hunger of the soul.
He was twice married—in 1887 and 1911. By his first wife, Marie Merck, he had two sons and twin daughters, and by his second wife, Margaret von Hoesslin, another son. His domestic life was afflicted by sorrows which undoubtedly left their mark in his brooding countenance. His two daughters died soon after marriage, while a talented son lost his life in the war. Another son was wounded, but lived to become Secretary of State to the Chancellor in the von Papen Government.
With his wife he visited England in 1946, on the occasion of the Royal Society Newton celebrations, and they were obviously much gratified by the respectful attention shown to them by England’s leading men of science. Although physically feeble, the great man showed on that occasion a lively interest in all that was going on, and spoke with clear memory and affection of his former visits to England.
Saturday, September 29, 2007
Introduction to physics
Physics is the science of matter and its motion—the science that deals with concepts such as force, energy, mass, and charge. It is the general analysis of nature, conducted in order to understand how the world around us behaves.
In one form or another, physics is one of the oldest academic disciplines; through its modern subfield of astronomy, it may be the oldest of all. Sometimes synonymous with philosophy, chemistry and even certain branches of mathematics and biology during the last two millennia, physics emerged as a modern science in the 17th century and these disciplines are now generally distinct, although the boundaries remain difficult to define.
Advances in physics often translate to the technological sector, and sometimes influence the other sciences, as well as mathematics and philosophy. For example, advances in the understanding of electromagnetism have led to the widespread use of electrically driven devices (televisions, computers, home appliances etc.); advances in thermodynamics led to the development of motorized transport; and advances in mechanics led to the development of the calculus, quantum chemistry, and the use of instruments like the electron microscope in microbiology.
Today, physics is a broad and highly developed subject. Research is often divided into four subfields: condensed matter physics; atomic, molecular, and optical physics; high energy physics; and astronomy and astrophysics. Most physicists also specialize in either theoretical or experimental research, the former dealing with the development of new theories, and the latter dealing with the experimental testing of theories and the discovery of new phenomena. Despite important discoveries during the last four centuries, there are a number of open questions in physics, and many areas of active research.
In one form or another, physics is one of the oldest academic disciplines; through its modern subfield of astronomy, it may be the oldest of all. Sometimes synonymous with philosophy, chemistry and even certain branches of mathematics and biology during the last two millennia, physics emerged as a modern science in the 17th century and these disciplines are now generally distinct, although the boundaries remain difficult to define.
Advances in physics often translate to the technological sector, and sometimes influence the other sciences, as well as mathematics and philosophy. For example, advances in the understanding of electromagnetism have led to the widespread use of electrically driven devices (televisions, computers, home appliances etc.); advances in thermodynamics led to the development of motorized transport; and advances in mechanics led to the development of the calculus, quantum chemistry, and the use of instruments like the electron microscope in microbiology.
Today, physics is a broad and highly developed subject. Research is often divided into four subfields: condensed matter physics; atomic, molecular, and optical physics; high energy physics; and astronomy and astrophysics. Most physicists also specialize in either theoretical or experimental research, the former dealing with the development of new theories, and the latter dealing with the experimental testing of theories and the discovery of new phenomena. Despite important discoveries during the last four centuries, there are a number of open questions in physics, and many areas of active research.
Absorption spectra of elements
A related phenomenum to the emission spectra of elements is the absorption spectra. Imagine that we have an electron in a lower energy state, and a photon comes along. If this photon has just the right amount of energy, it can be absorbed, causing the electron to make a transition to a higher energy state.
This will only occur though if the photon has an energy equal to the energy difference between the two levels involved in the transition - if not, the photon will just pass through.
Such an effect can be seen by shining light of all different frequencies through a gas of a particular element. Some of the photons will be absorbed in the gas, and so will be missing in the light that emerges from the gas. What one will therefore see from the emerging light is an almost continuous band of frequencies, but with some frequencies missing corresponding to the absorbed photons.
As with the emission spectrum, each element has its own unique absorption spectrum, as the energy levels of different elements differ. Measuring the absorption spectrum can therefore be used to identify elements in an unknown substance by comparing it to the spectrum of known elements. Among other areas, this is a major technique used to identify elements in gaseous clouds in galaxies.
This will only occur though if the photon has an energy equal to the energy difference between the two levels involved in the transition - if not, the photon will just pass through.
Such an effect can be seen by shining light of all different frequencies through a gas of a particular element. Some of the photons will be absorbed in the gas, and so will be missing in the light that emerges from the gas. What one will therefore see from the emerging light is an almost continuous band of frequencies, but with some frequencies missing corresponding to the absorbed photons.
As with the emission spectrum, each element has its own unique absorption spectrum, as the energy levels of different elements differ. Measuring the absorption spectrum can therefore be used to identify elements in an unknown substance by comparing it to the spectrum of known elements. Among other areas, this is a major technique used to identify elements in gaseous clouds in galaxies.
Friday, September 28, 2007
Alpha scattering experiment
Experiment to Scatter Alpha Particles
In 1909 Hans Geiger and Ernest Marsden observed that occasionally alpha particles are deflected through large angles when they strike a thin leaf of gold, even though most had passed through the leaf with little or no deviation. This scattering experiment led to Ernest Rutherford's nuclear theory of atomic structure, which was the first to describe the atom's positive charge as being concentrated in a dense nucleus around which negatively charged electrons circle.
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