Origin of Quantum Theory UNIT 1 Origin of Quantum Theory

Quantum Theory Quantum theory is a theory needed to describe physics on a microscopic scale, such as on the scale of atoms, molecules, electrons, protons, etc. Classical theories: Newton – Mechanical motion of objects (F = ma) Maxwell – Light treated as a wave NEITHER OF THESE THEORIES QUITE WORK FOR ATOMS, MOLECULES, ETC. Quantum Any of the very small increments or parcels into which many forms of energy are subdivided. Light is a form of energy is a quantum of EM energy

The Electromagnetic Spectrum Shortest wavelengths (Most energetic photons) E = hn = hc/l h = 6.6x10-34 [J*sec] (Planck’s constant) Longest wavelengths (Least energetic photons)

The Wave – Particle Duality OR

Light Waves Until about 1900, the classical wave theory of light described most observed phenomenon. Light waves: Characterized by: Amplitude (A) Frequency (n) Wavelength (l) Energy of wave a A2

Problem In the early 20th century, several effects were observed which could not be understood using the wave theory of light. Two of the more influential observations were: 1) The Photo-Electric Effect 2) The Compton Effect

The Photoelectric Effect

The phenomenon of ejection of electrons from a metal surface when illuminated by light or any other radiation of suitable wavelength (or frequency) The electrons ejected from the metal surface are called “photoelectrons”

The Experimental Setup An adjustable voltage is applied. Voltage can be forward or reverse biased (which slows down the electrons) Photoelectrons return to cathode through an ammeter which records the current

Effect of frequency: The minimum frequency required for the photoelectric emission to commence is called Threshold frequency. It depends on material and nature of surface of material. Effect of intensity of light: Photoelectric current is directly proportional to the intensity of light, provided frequency is more than threshold frequency.

Current vs. Bias voltage Low intensity (dim) High intensity (bright) Stopping potential Reverse bias Forward bias

Stopping voltage vs. Frequency (c/l) eV(stopping) frequency The stopping potential α Frequency of incident light

Laws of photoelectric emmission For each emitter surface, there is a certain minimum frequency called threshold frequency below which the emission does not take place. For frequency greater than threshold frequency, the magnitude of photoelectric current is proportional to the intensity of incident light The rate of emission of photo electrons is independent of its temperature The stopping potential is proportional to frequency but independent of intensity of light The photo electric emission is instantaneous. Time lag < 10-9 second The maximum K.E. increases with increase in frequency of incident light but independent of intensity.

Einstein’s theory of Photoelectric Effect Einstein suggested that light consisted of discrete units of energy E = hυ Electrons could either get hit with and absorb a whole photon, or they could not. There was no in-between (getting part of a photon). If the energy of the unit of light (photon) was not large enough to let the electron escape from the metal, no electrons would be ejected. (Hence, the existence of cutoff.) If the photon energy were large enough to eject the electron from the metal (here, W is the energy necessary to eject the electron), then energy of the photon absorbed (hυ) goes into ejecting the electron (W) plus any extra energy left over which would show up as kinetic energy (KE).

Photoelectric Equation hυ = W + ½ mv2 hυ = W + eV where υ is the frequency of the light W is the “WORK FUNCTION”, or the amount of energy needed to get the electron out of the metal V is the stopping potential When Vs = 0, υ= υcutoff , and hυcutoff = W.

Summary of Photons Photons can be treated as “packets of light” which behave as a particle. To describe interactions of light with matter, one generally has to appeal to the particle (quantum) description of light. A single photon has an energy given by E =hv= hc/l, where h = Planck’s constant = 6.6x10-34 [J s] and, c = speed of light = 3x108 [m/s] l = wavelength of the light (in [m]) Photons also carry momentum. The momentum is related to the energy by: p = E / c = h/l

The Electromagnetic Spectrum Shortest wavelengths (Most energetic photons) E = hn = hc/l h = 6.6x10-34 [J*sec] (Planck’s constant) Longest wavelengths (Least energetic photons)

Compton Effect

Incident X-ray wavelength Scattered X-ray wavelength The Compton Effect In 1924, A. H. Compton performed an experiment where X-rays impinged on matter, and he measured the scattered radiation. Compton M A T E R Incident X-ray wavelength l1 l2 > l1 Scattered X-ray wavelength l2 e Electron comes flying out Problem: According to the wave picture of light, the incident X-ray should give up some of its energy to the electron, and emerge with a lower energy (i.e., the amplitude is lower), but should have l2=l1.

Classical picture: oscillating electromagnetic field causes oscillations in positions of charged particles, which re-radiate in all directions at same frequency and wavelength as incident radiation. Change in wavelength of scattered light is completely unexpected classically Incident light wave Oscillating electron Emitted light wave θ Before After Electron Incoming photon scattered photon scattered electron

Conservation of energy Conservation of momentum θ Before After Electron Incoming photon scattered photon scattered electron Conservation of energy Conservation of momentum From this Compton derived the change in wavelength

COMPTON SCATTERING Compton (1923) measured intensity of scattered X-rays from solid target, as function of wavelength for different angles. He won the 1927 Nobel prize. X-ray source Target Crystal (selects wavelength) Collimator (selects angle) θ Detector

At all angles there is also an unshifted peak. This comes from a collision between the X-ray photon and the nucleus of the atom Result: peak in scattered radiation shifts to longer wavelength than source. Amount depends on θ (but not on the target material).