Chp 18: Quantum Flashcards
define Photoelectric Effect:
The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when the incident electromagnetic radiation of frequency higher than the threshold frequency is incident on the surface.
Observations of the Photoelectric Effect:
1) Existence of threshold frequency
2) Instantaneous emission of photoelectrons
3) Stopping potential is independent of intensity of incident EM radiation but dependent on frequency.
define Photon:
A photon is a quantum of electromagnetic radiation whose energy, E is equal to hf, where h is the planck’s constant and f is the frequency of electromagnetic radiation.
define Work function:
The work function of a metal is defined as the minimum amount of energy required for a free electron to escape from the surface of the metal.
define Threshold frequency:
It is the minimum frequency of incident radiation required to cause the emission of photoelectrons from metal surface.
define Ionization energy:
The minimum energy required to remove the outermost electron from the atom.
define Heisenberg Uncertainty Principle:
It states that the product of the uncertainty of measurement of the position and momentum of a particle can never be smaller than the planck’s constant, h.
Observation of Photoelectric Effect and how it proves that light behaves as Photons?
- Existence of threshold frequency Wave Theory:
Even if frequency is low by E = Pt, the electrons should be able to accumulate sufficient energy given enough time then gets emitted regardless of the intensity or frequency of incident light, there should not be a minimum frequency.
Quantum Theory: Due to the 1 to 1 photon-electron interaction, the photon requires a minimum energy that is greater than the work function of the metal such that a photoelectron can be emitted from the metal surface. Hence if the photon has a smaller energy than the work function, the photoelectron will not be emitted. By E=hf, the frequency must be larger than a minimum frequency known as the threshold frequency.
Observation of Photoelectric Effect and how it proves that light behaves as Photons?
- Maximum kinetic energy and Stopping potential is independent of the intensity of incident EM radiation
Wave Theory: As intensity of light increases, the electron absorbs greater energy which should mean that the photoelectrons will be emitted with greater kinetic energy, hence the maximum kinetic energy of the photoelectrons should increase.
Quantum Theory: By increasing the intensity of incident radiation, this only increases the number of photons arriving at the metal surface per unit time. However, since E=hf, each photon still has the same energy, as such, due to the 1 to 1 photon-electron interaction, the electrons still absorb the same amount of energy from 1 photon, it should be emitted with the same maximum kinetic energy. However, more photoelectrons are emitted per unit time.
Observation of Photoelectric Effect and how it proves that light behaves as Photons?
- Instantaneous emission of electrons
Wave Theory: At low intensities, electrons would need a significant amount of time to accumulate enough energy before it gets emitted, there should be a measurable time-lag for the emission of electrons.
Quantum Theory: Due to the 1 to 1 photon-electron interaction, so long as the energy of photon is larger than the work function of the metal, the electrons should be emitted instantaneously regardless of the intensity of incident EM radiation.
Why are photoelectrons emitted with a range of KE?
Electrons that are deep below the surface of the metal require additional work done against the interactions with the metal lattice as they collide with the metal lattice to be brought to the metal surface. The deeper the electrons, the lesser the KE they will be emitted with.
Why for certain values of V, the photocurrent detected is zero?
When the values of V are below the stopping potential, photoelectrons with the most KE cannot reach the collector as they experience a repulsive electric force. Since current is proportional to the rate of arrival of photoelectrons, no current is detected.
State in terms of energy changes the required condition for electromagnetic radiation to cause electrons to be emitted from the surface of metal. (Photoelectric effect)
The energy of the incident photon must be larger than the work function of the metal. The difference between the energy of incident photon and the work function of the metal is the maximum kinetic energy of the photoelectrons emitted.
Explain in terms of energy changes of the emitted photoelectrons, why there is a minimum potential difference (stopping potential) to reduce the photocurrent to zero.
There is a minimum potential difference as that is the potential difference which allows the electrons emitted with the most kinetic energy to convert all their kinetic energy to electrical potential energy just before reaching the collector. Since no electrons can reach the collector, there will be no current registered.
Explain why the current does not continue to increase for positive values of potential difference in the photoelectric effect.
Saturation current occurs when all the emitted electrons reach the collector per unit time. Increasing the V after saturation current occurs does not change the number of electrons emitted per unit time from the emitter and hence the number of electrons per unit time arriving at the collector does not change and the current does not change.
Observations to show the wave-particle duality:
- Light behaves as a wave
- Light behaves as particles
- Electrons behave as particles
- Electrons behave as a wave
- Interference / Diffraction of light
- Photoelectric effect
- Electrons undergo collision, have mass and charge
- Electron diffraction
What is the difference in terms of exciting an electron to a higher energy level using collision of incident electrons vs absorption of photons?
Electron collision: When an incident electron has energy equal or higher than the energy level difference required for the transition, the incoming electron can transfer part of its KE to the bounded electron in the atom for it to transit to a higher energy level. The remaining energy (KE of incoming electron minus energy level difference of that transition) is then remained as KE of the incoming electron.
Photon absorption: When an incident photon has equal energy to the energy level difference of a transition, the bounded electron in the atom can absorb the photon then transit to a higher energy level. This process only works if the photon energy is exactly equal to the energy level difference of that transition. If not, the photon will not be absorbed at all.
How an emission spectrum may be explained on the basis of the existence of discrete energy levels in atoms?
The coloured lines in the emission spectrum are clear and distinct with each line corresponding to a specific wavelength and frequency. As the electrons of an atom are at a higher excited state, it transits down, emitting a photon whose energy equals to the energy level difference of that transition. Since E=hf=hc/λ, since the energy levels are discrete, the photons emitted will have discrete energy hence discrete wavelengths.
A beam of white light passes through a cold gas. Spectrum of dark lines occurs. Explain why these dark lines occur (Absorption spectrum)
White light consists of light of various wavelengths ranging from 400nm to 700nm. When the energy of an incoming photon matches the energy level difference of a particular transition, a photon will be absorbed, which excites the electron, the electron transits to a higher energy level. The photons which have energy that do not match the energy level differences of the gas will pass through to the diffraction grating, forming the coloured background. As the electrons de-excite, they will emit photons with energy equal to the energy level difference of that transition in random directions. Since the energy levels are discrete, by E= hc/λ, the photons emitted have discrete wavelengths and the intensity of these emitted photons are small relative to the original white light, which causes clear and distinct dark lines on the coloured background.
Describe emission spectrum:
When a gas is heated or a potential difference is supplied to the gas, the electrons are excited, they transit to higher energy levels. As the excited electrons are unstable, they transit down to the lower energy levels, emitting a photon of energy equal to that of the energy level difference of that particular transition. Since the energy levels are discrete, the photons emitted have discrete energies, by E= hc/λ, thus discrete wavelengths. As the photons are incident on a diffraction grating, clear and distinct coloured lines will be formed on a dark background.
Describe the appearance of a visible line emission spectrum.
Clear and distinct coloured lines on a dark background.
How does the line spectra provide evidence for discrete energy levels in isolated atoms?
Excited electrons in the atom transit down, emitting photon of energy equal to that of the energy level difference of that transition. Since clear and distinct lines are seen with each line corresponding to a specific wavelength, this implies that the photons have discrete wavelengths, E=hc/λ, the photons have discrete energies. Therefore, this implies that the energy level difference in the gas atoms is discrete, hence the energy levels in the gas atoms are discrete.
Explain the origins of continuous spectrum, characteristic lines and cut-off wavelength in X-ray production.
Continuous spectrum: The incoming electron with high KE interacts with the target atom and decelerates, it produces an X-ray photon of energy equal to the kinetic energy lost by the incident electron due to braking radiation. After the interaction, the electron can undergo subsequent interaction with the target atoms again, undergoing different decelerations hence producing X-ray photons of different energies hence wavelengths.
Characteristic lines: When the incoming electron has sufficient energy, it can knock out a deep-lying inner shell electron from the target atom, leaving a vacancy. Electrons from outer shells can undergo a downward transition to achieve stability, emitting an X-ray photon of energy equal to that of the energy level difference of that transition.
Minimum wavelength: When the electron interacts with the target atom and comes to a stop, it transfers all of its KE into the energy of the X-ray photon emitted. Hence the minimum wavelength corresponds to the maximum energy of the X-ray photon emitted. (E=hc/λ)
In X-ray production, suggest 2 important properties of the materials used for the cathode (the filament) and the target.
Cathode:
1. A low value for its work function so that electrons can escape from its surface easily.
2. A low heat capacity so that less heat is required to raise its temperature.
Target:
1. A high melting point to withstand the large amounts of heat produced when electrons bombard it.
2. Has high atomic number so that it is more efficient in the production of X-rays,
3. A good conductor of heat so that heat can be removed from it easily.
