INTRODUCTION TO QUANTUM MECHANICS Flashcards
Scientific Concepts (CLASSICAL MECHANICS)
- Thermodynamics
- Harmonic and oscillations
- Work and energy
- Rotational motion
- Conservation laws
- Kinematics (motion w/o considering forces)
- Law of universal gravitation
- Fluid mechanics
What are the 3 unexplainable experiments?
- Blackbody spectrum
- Photoelectric effect
- Bright line spectra
Blackbody spectrum
Classical physics predicted that the intensity of radiation emitted by a blackbody at high frequencies (short wavelengths) would increase indefinitely, leading to the “ultraviolet catastrophe.” However, experimental data shoed a peak in intensity at a certain wavelength, which classical theories could not explain.
Photoelectric effect
Classical theories suggest that the energy of emitted electrons in the photoelectric effect should depend on the light’s intensity, regardless of its frequency. However, experiments showed that electrons were only emitted if the light had a frequency above a certain threshold, regardless of intensity.
Bright line spectra
Classical mechanics and electromagnetism failed to explain why atoms emit light at specific, discrete wavelengths, as seen in the emission spectra of elements.
Wave
a vibrating disturbance by which energy is transmitted
Wavelength l (lambda)
distance between identical points on successive waves
characterize by their length and height and by the number of waves that pass through a certain point in 1 second.
Frequency n (nu)
number of waves that pass through a particular point in 1 second.
Amplitude
vertical distance from the midline of a wave to the peak or trough
Blackbody spectrum
- there is continual shift of color as a body is heated to a higher temperature
- in terms of frequency, the radiation emitted goes from a lower frequency to a higher frequency as the temperature increases
- The exact frequency spectrum emitted by a bod depends on the particular body itself
All bodies, no matter how hot or old (T > 0 K) continuously radiate electromagnetic radiation.
- Human body at about 300 K
- emit EM radiation in the IR region (invisible to the naked eye)
Blackbody
an ideal body that absorbs and emits all frequency
Blackbody radiation
radiation emitted by a blackbody
3 Characteristics established upon extensive study of the blackbody radiation
- The total intensity, I (the average rate of radiation of energy per unit surface area) emitted from the surface of an ideal radiator is proportional to the fourth power of the absolute temperature.
- The intensity is not uniformly distributed over all wavelengths. Each has a peak wavelength at which the emitted intensity per wavelength interval is largest.
- experiment shows that lambda max is inversely proportional to T. (Wien’s displacement law)
- Experiments show that the shape of the distribution function is the same for all temperatures.
According to classical mechanics, each normal mode (oscillators of the field) shares equally in the energy supplied by the walls, so even the highest frequencies ae excited.
The Big Problem
Prediction of Rayleigh and Jeans
- a hot object should emit an infinite amount of energy in the ultraviolet range, but in real life, this doesn’t happen. The radiant energy density diverges as v^2
ULTRAVIOLET CATASTROPHE
Implicit in the derivation o Rayleigh and Jeans is the assumption that the energies of the oscillators responsible for the emission of the radiation could have any value whatsoever.
Planck
made the revolutionary assumption that the energies of the oscillators were discrete and had to be proportional to an integral multiple of the frequency.
The Planck Distribution Law can be used to justify the empirical relationships:
a. Stefan-Boltzmann law
b. Wien’s Displacement law
STUDY THIS
If Planck’s quantum hypothesis is correct, why are its effects not obvious in our daily life?
- Planck’s constant, 6.626 x 10^-34 is an extremely small number
- A quantum of energy, hv, is an extremely small amount
Planck’s rules regarding the gain or loss of energy are always the same, whether we are concerned with objects on the scale of our ordinary experience or with microscopic objects.
Photoelectric effect
German physicist Heinrich Hertz discovered that ultraviolet light causes electrons to be emitted from a metallic surface. The ejection of electrons from the surface of a metal by radiation is called the photoelectric effect.
(SEARCH)
How do we expect the photocurrent to depend on the voltage across the electrodes and the frequency and intensity of the light?
Based on Maxwell’s picture of light as an electromagnetic wave, it is expected that,
- The intensity of an electromagnetic wave depends on its amplitude but not its frequency. So the photoelectric effect should occur for any light of any frequency and the magnitude of the photocurrent should not depend on the frequency of the light.
- If the light falling on the surface is very faint, some time may elapse before the total energy absorbed by the surface equals the work function. Hence, for faint illumination, we expect a time delay between when we switch on the light ad when the photoelectrons appear.
- Because the energy delivered to the cathode surface depends on the intensity of the illumination, we expect the stopping potential to increase with increasing light intensity. Since intensity does not depend on frequency, we further expect that the light stopping potential should not depend on the frequency of light.
It takes a certain minimum amount of energy, called the work function to eject a single electron from a particular surface.
Experimental result:
- No matter how intense the light is, no current flows if the frequency is below the threshold frequency, and no photoelectric current is produced.
- No matter how weak the light, there is a photoelectric current if v > vo
- the magnitude of the photoelectric current is directly proportional to the intensity of the light so that the number of photoelectrons increases with the intensity of the incident light (therefore, we can associate light intensity with the number of photons arriving at a point per unit time)
Threshold frequency depends on the metal
Experimental Result:
- The kinetic energy of the ejected electrons is independent of the intensity of the incident radiation
- above the v0 the kinetic energy of the ejected electrons varies linearly with the frequency v.
- the slope of the line, vs vs. v (whatever the metal) is equal to Planck’s constant from the blackbody radiation.
Planck had applied his energy quantization concept to the emission and absorption mechanism of the atomic electronic oscillators; believed that once light energy was emitted, it behaved like a classical wave.
Einstein proposed instead that the radiation itself existed as small packets of energy, photons.
Einstein
showed that the kinetic energy of an ejected electron is equal to the energy minus the minimum energy required to remove an electron from the surface of a particular metal, called the work function.
