INTRODUCTION TO QUANTUM MECHANICS

Question 1

Scientific Concepts (CLASSICAL MECHANICS)

Answer 1

• Thermodynamics
• Harmonic and oscillations
• Work and energy
• Rotational motion
• Conservation laws
• Kinematics (motion w/o considering forces)
• Law of universal gravitation
• Fluid mechanics

Question 2

What are the 3 unexplainable experiments?

Answer 2

1. Blackbody spectrum
2. Photoelectric effect
3. Bright line spectra

Question 3

Blackbody spectrum

Answer 3

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.

Question 4

Photoelectric effect

Answer 4

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.

Question 5

Bright line spectra

Answer 5

Classical mechanics and electromagnetism failed to explain why atoms emit light at specific, discrete wavelengths, as seen in the emission spectra of elements.

Question 6

Wave

Answer 6

a vibrating disturbance by which energy is transmitted

Question 7

Wavelength l (lambda)

Answer 7

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.

Question 8

Frequency n (nu)

Answer 8

number of waves that pass through a particular point in 1 second.

Question 9

Amplitude

Answer 9

vertical distance from the midline of a wave to the peak or trough

Question 10

Blackbody spectrum

Answer 10

• 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

Question 11

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)

Question 12

Blackbody

Answer 12

an ideal body that absorbs and emits all frequency

Question 13

Blackbody radiation

Answer 13

radiation emitted by a blackbody

Question 14

3 Characteristics established upon extensive study of the blackbody radiation

Answer 14

1. 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.
2. 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)

3. Experiments show that the shape of the distribution function is the same for all temperatures.

Question 15

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.

Question 16

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

Question 17

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.

Question 18

Planck

Answer 18

made the revolutionary assumption that the energies of the oscillators were discrete and had to be proportional to an integral multiple of the frequency.

Question 19

The Planck Distribution Law can be used to justify the empirical relationships:

Answer 19

a. Stefan-Boltzmann law
b. Wien’s Displacement law

STUDY THIS

Question 20

If Planck’s quantum hypothesis is correct, why are its effects not obvious in our daily life?

Answer 20

1. Planck’s constant, 6.626 x 10^-34 is an extremely small number
2. A quantum of energy, hv, is an extremely small amount

Question 21

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.

Question 22

Photoelectric effect

Answer 22

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.

Question 23

(SEARCH)

How do we expect the photocurrent to depend on the voltage across the electrodes and the frequency and intensity of the light?

Question 24

Based on Maxwell’s picture of light as an electromagnetic wave, it is expected that,

Answer 24

1. 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.
2. 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.
3. 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.

Question 25

It takes a certain minimum amount of energy, called the work function to eject a single electron from a particular surface.

Question 26

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)

Question 27

Threshold frequency depends on the metal

Question 28

Experimental Result:

Answer 28

* 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.

Question 29

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.

Question 30

Einstein proposed instead that the radiation itself existed as small packets of energy, photons.

Question 31

Einstein

Answer 31

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.