19 Quantum Flashcards
Definition of photoelectric effect
The emission of photoelectrons from a metal surface when electromagnetic radiation of a sufficiently high frequency is incident on it.
How to tell if photoelectric emission has occurred at the emitter?
The ammeter registers a current due to the electrons from the emitter reaching the collector and completing the circuit.
What is the purpose of adjusting the variable DC supply?
The potential of the collector is made more positive or negative with respect to the emitter to accelerate or decelerate the emitted electrons.
Relationship between stopping potential and intensity of incident light
The two are independent.
Relationship between photoelectric current and intensity of incident light
The two are proportional.
Definition of a photon
A photon is a small discrete quanta of electromagnetic energy from a beam of light.
Formula for energy of a single photon E
E = hf = hc/λ
Planck constant h = 6.63 x 10^-34
Electron-volt eV = 1.6 x 10^-19 (same as elementary charge)
E is proportional to f.
Definition of work function Φ
The minimum amount of energy that will remove an electron from the surface of the metal.
Formula for work function Φ
Φ = hf0 = hc/λ0
Definition of threshold frequency f0
The minimum frequency of an incident photon that will remove an electron from the surface of the metal.
Note:
A photon’s energy cannot be shared among multiple electrons, one electron can only absorb one photon.
Einstein’s equation for photoelectric effect (energy conservation)
E = Φ + Ekmax
Definition of stopping potential Vs
The minimum potential difference between the metal and collector that will prevent an ejected photoelectron from reaching the collector.
Formula for stopping potential, Vs
Ekmax = 1/2 mvmax^2 = eVs
Graph of stopping potential against frequency of incident light: y = Vs x = f m = h/e y-intercept = -Φ/e x-intercept = f0
Formula for intensity of incident radiation I
I = power/area = (energy/time)/area = [(Np/t)(hf)]/A = (Np/t)(hf/A)
Np/t = rate of photon arrival on metal surface
Definition of saturation current
Formula for saturation current isat
At saturation current, all photoelectrons emitted will reach the collector
isat = Q/t = Nee/t = (Ne/t)e
Ne/t = rate of photoelectron emission from metal surface
Explanation for existence of threshold frequency
Wave theory:
Photoelectric emission occurs for any frequency of monochromatic incident light.
Energy transfer is continuous, electrons accumulate energy until it has sufficient to escape.
Quantum theory:
Energy of incident photon must be larger than work function of metal for photoelectric emission to occur.
Increasing intensity of monochromatic incident light only increases number of photons arriving on metal surface per unit time, energy of each photon is not affected.
Explanation for no time delay in emission of photoelectrons
Wave theory:
At low intensity light, there is less energy, electrons need time to accumulate sufficient energy to escape metal surface, causing time lag between emission of photoelectrons and incidence of light on surface.
Quantum theory:
For frequencies of incident photons more than threshold frequency of target metal, energy of photon is sufficient to overcome work function of metal to be ejected.
Photoelectrons are emitted immediately after light is incident on metal surface regardless of intensity.
Electrons cannot accumulate energy through absorption of multiple photons, each can only absorb one.
Explanation for stopping potential independent of intensity of incident light
Wave theory:
Increasing incident light intensity causes greater amount of incident energy on surface, giving liberated electrons more energy.
Maximum kinetic energy possessed by ejected photoelectrons increases, stopping potential increases.
Quantum theory:
Increasing incident light intensity at constant frequency causes higher photon arrival rate.
Energy of each incident photon is unchanged.
Each photoelectron is liberated by one photon, maximum kinetic energy possessed by ejected photoelectron is unchanged, stopping potential is unchanged.
Explanation for photocurrent proportional to intensity of incident light
Wave theory:
Intensity of wave is energy incident per unit area per unit time.
More incident energy liberates more electrons, increasing photocurrent.
Quantum theory:
Higher intensity of incident light of constant frequency causes greater number of photons arriving on metal surface per unit time.
More ejected photoelectrons per unit time, increasing photocurrent.
Formula for de Broglie wavelength
λ = h/p = h/mv
How does the existence of line spectra provides evidence for existence of discrete electron energy levels in isolated atoms
Each line on the line spectrum corresponds to a single wavelength, hence a single frequency of light
Energies of photons emitted are discrete
Since energy level of photons correspond to energy difference between two energy levels in an atom,
Energy levels of electrons within the atom are discrete as well
Emission line spectrum
When a high potential difference is applied across a discharge tube containing the gas at low pressure the atoms of the gas are excited through inelastic collisions
Excited atoms are highly unstable and will quickly de-excite to lower energy states
Excited atoms emit photons while de-exciting
Absorption line spectrum
White light consisting of photons of a continuous range of frequencies passes through a discharge tube containing the gas at low pressure and temperature
Photons which have the energies that correspond to the energy difference between two discrete energy levels are absorbed,
causing electrons to be excited from ground state to higher levels and subsequently de-excite, emmiting photons of similar energies to those absorbed randomly in all directions.
Hence the intensity of these photons is reduced, forming dark lines
Heisenberg uncertainty principle
The heisenberg Uncertainty Principle states that it is impossible to measure the exact position and momentum at the same time
△x △p ≥ h
