The following experimental observations (between 1895 and 1911) needed new quantum ideas:

Transcription

1 The following experimental observations (between 1895 and 1911) needed new quantum ideas: 1. Spectrum of Black Body Radiation: Thermal Radiation 2. The photo electric effect: Emission of electrons from metals by light 3. Stability of the Nuclear Atom 4. Discrete nature of light spectra of atoms 5. Radioactivity spontaneous emission of particles and radiation from atoms, giving rise to atomic transmutation. concepts Introduced: Quantum Lumps photons E = hf Planck/Einstein Quantum Jumps Transitions between allowed energy states. hf(2 to 1) = E2 E1... Bohr Wave particle duality(de Broglie) quantum mechanics (Schroedinger, Heisenberg and Born) Social and anti social identical particles : (Bosons and Fermions ) Weak and Strong forces (Weak for beta radioactivity and Strong for nuclear binding)

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3 Quantum Lumps Black body or Cavity Radiation : The cavity when heated to some temperature will emit light which comes out of the hole. The EM radiation is in equilibrium with the atoms in the walls of the cavity. The spectrum of light observed is independent of the material of the walls and only depends on the temperature. It has a universal shape. Perfect absorber and emitter.

4 Measurement of the spectrum in Principle spectrometer BB at Temp T Intensity measuring device Best measurements by Kirchoff and coworkers in the late 19th century

5 Shift of the peak position measured.

6 Experimental BB radiation spectrum: Universal Shape c f c f= f =c = C= speed of light = 300 million meters/sec

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8 Intensity versus wavelength T = 6000 K T =320 K visible Infra red Wavelength in microns Intensity versus frequency Universal Cosmic Background

9 Ultra violet Catastrophe in classical theory

10 A bold Conjecture of the Quantum (lump) of Radiation

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12 Black body radiation is produced by electrical atomic oscillators in the wall. To explain these observations quantitatively, Max Planck had to postulate that a vibrating charge emits radiation not continuously like water from a fire hose, but instead in lumps like baseballs from a pitching machine. The smallest non zero energy these lumps can have was proportional to the frequency of the oscillator. A quantum oscillator with characteristic frequency f 1 Planck said can only have definite energy values which are 0, hf 1, 2hf 1, 3hf 1,.... another oscillator having another frequency f 2 would have energies 0, hf 2, 2hf 2, 3hf 2,.... The first oscillator will emit or absorb only quanta of energy and the second oscillator will emit or absorb quanta of energy hf1 hf 2

13 This is measured curve for Cosmic Microwave Background radiation spectrum and the line is the fit using Max Planck's formula! Temperature of this CMBR corresponds to degrees Kelvin!

14 Max Planck's spectral formula for different temperatures Universal Curve Frequency in Hz Dashed line: Classical prediction gives infinity if summed over all frequencies

15 2. Photo electric effect: Emission of energetic electrons from some metals when light illuminated them. This emission had properties: Light is characterized by frequency or wavelength and intensity. 1. No electrons emitted below a certain frequency 2. The minimum frequency depended on the metal 3. For light with frequency higher than the minimum frequency (a) the max KE of emitted electrons was proportional to frequency. (b) the number of electrons emitted was proportional to light intensity

16 Number and Kinetic Energy of emitted electrons measured for light of different wavelengths on Potassium (K) metal.

17 Einstein's bold assumption Einstein assumed that light consists lumps called photons Light is defined by its frequency f Energy of light photon E=hf Max kinetic energy electron can have is KE =hf hf 0 where hf 0 is a characteristic binding energy for electrons in the material Einstein determined the value of h from experimental results of Lenard A typical Experiment

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19 So Einstein said that to explain the photoelectric effect light must be exhibiting particle like properties, even though it had been shown to be an Electro Magnetic wave At this time the structure of the atom had not been elucidated by Rutherford with his alpha scattering experiments. Einstein did not discuss how these lumps or photons were created. The energy of individual photons is so small that when light from a bulb impinges upon you so many photons are hitting your eye per second that you do not sense the lumpiness of light.

20 3. The Nuclear Atom Radioactive source of alpha particles

21 Scatter.html Plum pudding model could never scatter an alpha particle through large angles Nuclear model would scatter backwards. Detailed study can measure nuclear charge and nuclear radius. Rutherford's nuclear model is shown schematically in the next slide.

22 Atom Magnified Mostly empty space! Electrons 10 kilometers Electric Force e +Ze Nucleus 1 meter in size Mass of the atom Contains protons and neutrons

23 Inside the Nucleus of the atom of element Lithium Four neutrons and three protons Neutron Proton Protons have positive electric charge Atomic mass 7 Atomic charge 3 Held together by Strong nuclear force Neutrons are electrically uncharged

24 The Bohr Atom Rutherford's atom was mostly empty space with electrons moving around the nucleus. Classical Physics (E and M) said that accelerated charges radiated away electro magnetic energy. If the electron was moving around the nucleus in orbits it would spiral into the nucleus in a very short time. Bohr was a young Danish theoretical physicist who came to spend some time with Rutherford in Manchester. He began to worry about stability of the atom and how it could radiate. He had three key insights that set him on the right path.

25 Bohr had to make the hydrogen atom stable and he should be able to calculate the observed spectrum of light emitted by the atom. Hydrogen spectrum Balmer Series

26 Bohr' model gave the correct answers for the energy levels and agreed with Balmer's formula to better than a percent. His model was rather ad hoc, and was an incorrect picture but gave the right numbers!! He had three assumptions which were later superseded by quantum mechanics: 1. Electrons move in classical circular orbits 2. Electrons wont radiate while in these orbits 3. Electron jumps instantaneously from one orbit to another randomly when it radiates or absorbs light He surmized that Planck's constant ℏ= h 2 Was the natural unit for angular momentum for electrons in allowed orbits.

27 First was the key to stability of atoms. He argued that if the essence of quantum theory is that the system is allowed only certain values of the energy then there could be a LOWEST enegy level, below which the electron could not go. Lowest energy would be the GROUND STATE of the atom in which the atom would normally be found! Higher levels are those which can be excited if energy is supplied to the atom Second insight was that SOMETHING MUST SET THE SIZE OF THIS LOWEST ORBIT Bohr reasoned that it must depend on the mass and charge of the electron, m and e ; and if Quntum theory were to play a role then Plankc's constant,h, must also enter. He noted that the combination h2 2 has the units of length and it is me roughly in the range of atomic diameters Show this. Third insight was that an atom with a restricted set of energy levels could change its internal energy ONLY by moving from one allowed level to another Then it could emit light and Einstein relation E =h f would determine this discrete frequency!

28 He was reminded by his classmate H.M.Hansen of the formula guessed by Balmer to describe the observed spectral lines of hydrogen. Balmer Formula f = f n m2 for transition between energy levels n and m This formula looked very similar to that considered by Bohr 1 f = E n E m h Bohr quantized his orbits by quantizing the angular momentum, and introduced the quantum number n by mvr =n ℏ 2 e Then he used Classical physics to equate Coulomb' s force, 2 to r 2 mv Centrepetal force and calculated the energy of each level r He got the correct value of f 0 in Balmer's equation.

29 Atmoic radius given by Bohr ℏ 2 2 is very close to correct answer. me And his energy formula is very close to the exact relation E n= me 2ℏ ev n n2 = 2 which is very close to what is actually measured. The constants are: ℏ= ev sec ; and ev = Joule

30 Quantum Mechanics took shape in the 1920s. The most important persons in this development are: Louis de Broglie Matter waves Erwin Schroedinger Wave Equation Werner Heisenberg Matrix Mechanics Max Born Probability interpretation of the wave function Wolfgang Pauli Spin as an internal property exclusion principle Paul Dirac Relativistic wave equation and quantum field theory Bose/Einstein Social particles Integer spin no exclusion principle Fermi/Dirac Anti social particles half integer spin F D statistics

31 Erwin Schroedinger Louis de Broglie Max Born Werner Heisenberg

32 Wolfgang Pauli Satyendra Nath Bose Enrico Fermi

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