quantum model Flashcards
(26 cards)
What is a black body and what does it do?
A black body is an idealistic object that absorbs all radiation falling within its vicinity. A black body at thermal equilibrium and given temperature would also emit radiation of exactly the same amount as what it first absorbed.
Outline the classical theory of em radiation (rayleigh-jeans law)
The intensity of black body radiation is directly proportional to its frequency. The greater a black body’s temperature, more energy it emits.
How does the classical model disobey the LOCOE?
The classical model proposes that a black body at thermal equilibrium would emit radiation at all frequencies, resulting in an infinite amount of energy, disobeying the LOCOE
Outline Planck’s quantum theory to resolve the UV catastrophe
Planck suggested that energy was not continuous but rather quantised. That is, energy of light was confined to discrete amounts equal to integral multiples of a smallest unit of energy (a quantum). (E=hf)
What does Wien’s displacement law state?
The black-body radiation curve for different temperatures will peak at different frequencies/wavelengths. I.e. wavelength that produces the highest intensity varies inversely with temperature; higher the temperature, shorter the wavelength according to landermax = b/T(temp in kelvin)
What are the three main predictions regarding the photoelectric effect made by the wave model of light?
- Light with higher intensity will eject electrons with greater kinetic energy
- Light with higher frequency will result in a greater current
- Light of any intensity and frequency will be able to eject electrons
Outline Lenard’s Experiment on the Photoelectric Effect
He studied how the energy of the emitted photoelectrons varied with the intensity and frequency of light. He also measured the magnitude of current produced by the ejected electrons.
The variable light source was used to illuminate a positively charged metal plate (cathode) in an evacuated tube (vacuum). The ejected electrons, which are termed photoelectrons, were travelling towards the negatively charged metal (anode).
Outline how the number of photoelectrons were measured
When photoelectrons reach the anode, they flow through the wire from the anode back to the cathode. The galvanometer is used to measure the current, which is the amount of charge (electrons) flowing through it per second. When there are more photoelectrons reaching the anode, the magnitude of current will increases.
Outline how the kinetic energy of photoelectrons was measured
To measure the kinetic energy of the ejected electrons, Lenard applied a reverse voltage that does work against the liberated electrons’ motion. Thus, only electrons ejected with enough kinetic energy to overcome the work done by the electric field will reach the anode and flow through the galvanometer.
What is the stopping voltage?
It is the potential difference required to prevent photoelectrons from reaching the anode. The stopping voltage can be used to calculate the maximum kinetic energy of photoelectrons. (K(max)=q(e)V(stopping))
How were Lenard’s experimental observations inconsistent with predictions made by the wave model of light?
- He observed that increasing intensity of light did not increase the stopping voltage (a measure of photoelectrons’ kinetic energy). Instead, the photocurrent increased. However, the classical predicted that BOTH photocurrent and stopping voltage would increase.
- Increasing frequency did not increase the photocurrent but instead increased the stopping voltage.
- Light below a certain frequency was unable to liberate photoelectrons, no matter what the intensity of light was. There existed a threshold frequency - a minimum frequency required for photoelectrons to be ejected. This was inconsistent with the wave model, which predicted that the energy barrier for electrons to be ejected can simply be met by increasing the intensity of light.
Outline Einstein’s quantum model of light
- Light consists of photons.
- When a photon strikes a metal surface, it transfers its energy completely to one electron. The energy transfer only occurs when the photon’s energy exceeds the metal’s work function.
- Remaining amount of energy is transformed into a photoelectron’s kinetic energy.
- If a photon’s energy is less than the work function, no photoelectrons are emitted.
What are photons?
discrete packets of energy (mirroring Planck’s quanta)
What is the difference between Planck and Einstein’s idea of quantisation?
Planck still perceived light as a continuous, unbroken wave. In contrast, Einstein’s quantum model of light describes light as discrete packets of energy (photons).
What is work function?
In the photoelectric effect, work function (φ) is the minimum amount of energy required to remove an electron from the metal.
What is the condition for energy transfer between a photon and an electron to occur, and for photoelectrons to be ejected?
The energy transfer between a photon and an electron only occurs if the photon’s energy exceeds the metal’s work function. Since the energy of a photon depends on its frequency, a threshold frequency is required for photons to eject electrons. To eject photoelectrons, the electrostatic attractions within the metal must be overcome. As such, there must be a minimum amount of energy required.
What happens after the work function of the metal is overcome and why?
the remaining energy of a photon is transformed into a photoelectron’s kinetic energy due to the LOCOE, which implies that the energy required to liberate the electrons (work function) plus that in excess (kinetic energy) must equal that which was absorbed (energy of photon), therefore K(max) = hf − ϕ
What equation is the stopping voltage required to stop photoelectrons from reaching the anode given by?
q(e)V(stopping) = hf - ϕ
What happens when the electron is some distance into the material of the cathode (away from the surface)?
some energy will be lost as it moves towards the surface. This means the final kinetic energy possess by electrons ejected from deep down in the cathode will be lower. The most energetic electrons (greatest kinetic energy) emitted will be those very close to the surface.
How does Einstein’s quantum model of light explain the photoelectric effect?
In Einstein’s quantum model, light’s intensity is proportional to the number of photons. Thus, an increase in intensity corresponds to an increase in the number of photons emitted by the light source per second.
What is Lenard’s first observations as to how Einstein’s quantum model of light explains the photoelectric effect?
Lenard’s observation #1: light below a certain frequency cannot eject electrons regardless of its intensity
- A photon can only transfer its energy to an electron if its energy exceeds the metal’s work function.
- If light’s frequency is below the threshold frequency, no electrons are ejected.
- Intensity of light (number of photons) does not change the energy of one photon. An electron can only absorb energy from one photon only.
What are the features of the graph of Maximum Kinetic Energy vs Frequency?
- maximum kinetic energy of photoelectrons against frequency of light used to irradiate the metal
- gradient: Planck’s constant h.
- y-intercept: negative value of work function.
- x-intercept: threshold frequency of light required to produce the photoelectric effect.
- When a different metal is used, gradient remain unchanged, x and y-intercepts will change.
What are the features of the graph of Current vs Frequency?
- Below a certain frequency, no photoelectrons will be emitted because a photon does not have sufficient energy (less than the work function).
- When the frequency is above the threshold frequency, current is independent of frequency because number of photoelectrons emitted is unaffected by the energy (frequency) of a photon.
What are the features of the graph of Maximum Kinetic Energy vs Intensity?
- The maximum kinetic energy of photoelectrons is independent of the light’s intensity.
- Photoelectrons’ maximum kinetic energy depends on the energy of a single photon, which is determined by its frequency.
- Intensity of light (number of photons) does not affect the kinetic energy because an electron cannot absorb energy from more than one photon.
