Model Answers - Topic 5c - wave particle duality Flashcards
define the intensity of light in the wave model of light
intensity is power/area
intensity is proportional to the amplitude of the wave squared - this is related to the energy of the wave
define photon
discrete packet of electromagnetic energy
describe what is meant by the wave particle duality of light
o Light exhibits wave behaviour (eg. diffraction, intereference, superposition, polarisation)
o Light exhibits particle behaviour (eg. absorption and emission line spectra, photoelectric effect)
o So light exhibits both wave and particle behaviour: it exhibits wave particle duality
define work function
minimum energy required for electron to be released from the surface of a metal
define threshold frequency
minimum photon frequency required for electron to be released from the surface of a metal (by absorbing the photon)
explain how the equation hf = Φ + KEmax is a conservation of energy equation
o hf is the photon energy
o when the electron absorbs the photon, the photon energy is transferred to the electron
o the electron leaves the surface of the metal using a minimum amount of energy called the work function Φ
o The remaining energy is transferred into the kinetic energy of the electron
o Which will have a maximum value of KEmax when the electron has only used the work function to leave the surface
- Explain why the kinetic energy of the electron in the equation hf = Φ + KEmax is the maximum kinetic energy –
o the work function is the minimum energy required for electron to be released,
o thus in the equation hf = work function + ke max, the kinetic energy is the maximum possible kinetic energy.
o Most electrons will have less kinetic energy than this as they require more energy in order to leave the surface of the metal (due to needing more than the minimum energy to overcome the electrostatic forces of attraction).
plot a graph of maximum kinetic energy of released electron against frequency of photon
- say y intercept is negative work fucntion
derive the equation relating threshold frequency and work function
o The threshold frequency, f0 is the photon frequency that would cause electrons to just leave the metal surface but have no kinetic energy on escaping
o The equation hf = Φ + KEmax becomes
o hf0 = Φ where Φ is the work function
o so f0 = Φ / h
complete the table describing the:
observation from the photoelectric effect, what would be expected by the wave model, why this observation leads to the particle model of light
observation 1: electrons are released instantaneously from the metal surface
expectation 1: the energy would take time to be transferred from the light to the electron
model 1: one electron absorbs one photon, absorbing its energy as a packet
observation 2: the kinetic energy of electrons is dependent on the frequency of incident light
expectation 2: the kinetic energy of the electron should be dependent on the intensity of the light, as intensity is related to the energy of the light in the wave model
model 2: the energy of a photon equals hf
observation 3: only light above a certain threshold frequency value will cause electron emission
expectation 3: any frequency of light should release electrons as long as the intensity is high enough. energy in the wave model is dependent on intensity
model 3: the minimum photon energy to release an electron from the metal surface is equal to the work function, Phi, of the metal. this means there is a minimum threshold frequency f = phi/h required to release the electron
observation 4: increasing intensity of light increases the number of electrons emitted per second
expectation 4: increasing intensity should increase the energy of emitted electrons
model 4:
Intensity = power / area = rate of energy transfer per second/area
Intensity = number of photons x energy of one photon/ time x area
I = Nhf/tA
So the intensity is directly proportional to the number of photons per second
As one photon is absorbed by one electron, this is also proportional to the number of electrons released per second
explain how the photoelectric effect indicates that light is a particle
- In the wave model energy would be absorbed over time and so it would take time for electrons to be released – this is not observed
- Instead, it is observed in the photoelectric effect that electrons are emitted instantaneously from the metal
- This indicates that one photon is absorbed by one electron
- In wave model energy of the wave is proportional to intensity, so in the wave model the kinetic energy of the electrons should depend on intensity – this is not observed
- Instead, it is observed that the kinetic energy of the electron is only dependent on the frequency of the photon, not intensity
- So the energy of the photon, E=hf is proportional to frequency
- It is also observed that as intensity increases the number of electrons leaving the metal surface per second increases
- This is because more photons are absorbed each second as intensity increases
- In the wave model, high intensity light of any frequency should emit electrons – this is not observed
- Instead, it is observed that only EM radiation above a certain threshold frequency will release electrons
- Electrons are only released from the metal surface when energy of photon is larger than work function of metal
define the intensity of light in the particle model of light, deriving its equation and stating what it is proportional to
o Intensity = power / area = rate of energy transfer per second/area
o Intensity = number of photons x energy of one photon/ time x area
o I = Nhf/tA
o So the intensity is directly proportional to the number of photons per second
- State the effect on the maximum kinetic energy of photoelectrons emitted when the intensity of light increases
no effect
- State the effect on the number of photoelectrons emitted per second when the intensity of light increases
o The number of photoelectrons emitted per second increases in proportion with the intensity increase
- Draw a circuit diagram that we could use to determine the stopping potential (watch this video: https://www.youtube.com/watch?v=mXnTzcB3wFU
define stopping potential
a. The minimum potential difference at which photoelectrons do not have enough kinetic energy to pass across the gap
b. Vs = KEmax/e
- Define the de Broglie wavelength
a. The wavelength of a particle that has a momentum
b. λ = h/p where λ is the de Broglie wavelength, h is the Planck’s constant, p is the momentum of the particle
define energy level
the discrete allowed energy of an electron within an atom
explain why energy levels of electrons in atoms are negative
a. A just free electron has zero energy
b. In order for the electron to move up energy levels to be released it must gain energy
- Explain origin of line spectra (spectral lines/ emission lines) specific to certain elements at specific frequencies/wavelengths
a. Electrons exist in discrete energy levels
b. Electron within atom excited to higher energy level when: fast moving electron collides with atom, transferring its kinetic energy or current is passed through OR gas is heated
c. The electron then falls back down to lower energy level
d. Emitting a photon with an energy E equal to the energy difference, ΔE between the two electron levels
e. E=hf is the energy of the photon OR E = hc/λ is the energy of the photon
f. The photon is emitted with a specific frequency f = ΔE /h where ΔE is the energy difference between the levels OR The photon is emitted with a specific wavelength λ = hc/ ΔE where ΔE is the energy difference between the levels
g. There are only a limited number of energy differences between levels and there only a corresponding limited number of frequencies/wavelengths of photon emitted
h. Different elements have different energy differences between levels so produce different spectral lines
- Explain origin of absorption spectra at specific frequencies/wavelengths
a. Electrons exist in discrete energy levels
b. Electron within atom (eg. in atmosphere of sun) excited to higher energy level when it absorbs a photon
c. E=hf is the energy of the photon OR E = hc/λ is the energy of the photon
d. The photon absorbed must have a specific frequency f = ΔE/h where ΔE is the energy difference between the levels OR The photon absorbed must have a specific wavelength λ = hc/ΔE where ΔE is the energy difference between the levels
e. There are only a limited number of energy differences between levels and only a corresponding limited number of frequencies/wavelengths of photons absorbed
well done!! treat yourself :)
