Chapter 17. Quantum Physics Flashcards
Define the photoelectric effect
The photoelectric effect is a phenomenon in which electrons are liberated from a cool metal surface when electromagnetic radiation of sufficiently high frequency is incident upon it
- Define photon
2. Give the formula for its energy
- A photon is a quantum of electromagnetic radiation
2. Ephoton = hf = hc/λ where h is the Planck constant (h=6.63 *10^-34 Js) f is the frequency of the light c is the speed of light 3*10^8
What is the alternative unit for energy?
Electron volt (eV)
1 eV = 1.6 *10^-19 V
What is stopping potential Vs and saturation current Is?
- Vs - potential difference across the adjustable DC supply whereby even the most energetic photoelectrons could not reach the collector
(Frequency affects Vs)
- Measures KEmax = eVs - Is - Maximum rate of emission of photoelectrons from the transmitter as all the ejected photoelectrons reach the collector
(Intensity affects Is)
Define Work Function (Φ) of a metal. Give its formula
The work function is the minimum amount of energy required to remove an electron from the metal surface (energy required to remove the least strongly held electron)
hf = Φ + KEmax
Explain the instantaneous emission of photoelectrons
Each photon passes its entire quantum of energy to a single electron, enabling the electron to escape with no delay
What is the emission line spectra and what are the conditions for photons to be removed?
Collisions between the electrons and atoms results in transfer of energy from the electrons to the atoms and the atoms are excited from their ground state. Excited atoms are unstable and will quickly de-excite to lower energy states. May not de-excite to ground state, may take a series of jumps through intermediate energy states to the ground state, emitting more than 1 photon in the process.
f of emitted photon depends on the energy difference b/w Ei and Ef.
hf = Ei - Ef
Excess energy remains as the KE of the bombarding electron
Photons emitted in all directions whereas in emission line spectra photons are travel in one direction after passing through the collimator slit.
What is absorbtion line spectra?
Inverse of Emission line spectra. Photons incident on cool atomic vapour (atoms in ground state). If energy corresponds to the energy difference between the ground state and an excited state, it may be absorbed by the atom.
The atomic vapour therefore absorbs photons of specific energies/frequencies
What is observed on the screen is the original continuous spectrum emitted by the hot filament lamp with darker lines corresponding to the frequencies absorbed.
Photons emitted in all directions whereas in emission line spectra photons are travel in one direction after passing through the collimator slit.
What is present in the graph of a X-ray spectra?
- Continuous radiation (Bremsstrahlung)
2. Characteristic lines
Explain the continuous radiation (Bremsstrahlung)
- The energetic electrons decelerate as they hit the metal target.
- This loss in KE is manifested in the form of a photon
- Since the bombarding electrons can loss any fraction of its KE in a collision interaction with a metal atom, the photon emitted can take on ant value of energy
- The maximum energy the emitted photons can have, however is the entire KE of the bombarding electron
- Hence, hfmax = hc/λmin = eV
- The value of λmin therefore depends solely on the accelerating voltage V
Explain the characteristic lines
- Highly energetic bombarding electrons penetrate the atom and knock out an inner shell electron from a metal atom (The inner-most shell is K, followed by L, M, N etc)
- If a K-shell electron is removed, an electron from the L shell could fall into the vacancy in the K-shell, emitting a photon equivalent to the energy difference between the K and L shells. This is the Kα line.
- The Kβ line is produced by an M-electron falling into a K-shell vacancy.
- One could also have electrons from shells further away to fill a K-shell vacancy (these are not shown in the diagram)
- The positions of the peaks depend solely on the type of metal and its energy level intervals
- The wavelengths are so short because the energy differences between the inner-shells are very large (therefore it is in X-ray region)
Define Wave-Particle Duality
Waves can exhibit particle-like characteristics and particles can exhibit wave-like characteristics
Equation for de Broglie’s Hypothesis
λ = h/p = h/mv = h/ sqrt(2m(KE))
where p is the momentum of the particle
Equations for Heisenberg Uncertainty Principle
- ∆x∆p_x is greater than or equal to h/4π
∆x is uncertainty of position of a particle
∆p_x is the uncertainty of measurement of linear momentum - ∆E∆t is greater than or equal to h/4π
∆E is the uncertainty in the energy of the system
∆t is the time during which the system exists unperturbed
Equation for Quantum Tunneling
- T
- k
Transmission coefficient T
Reflection coefficient R
- T ∝ e^(-2kd)
2. where k =sqrt(2m(U-E))/ħ m = mass of particle U = barrier height E = total energy of the particle before penetrating the barrier ħ = h/2π
What are the things to note?
- Calculating frequency from work function (Φ)
- Work function in tunneling equals?
- What not to assume in wave particle duality regarding KE and momentum equation?
- Φ Must be in Joules, not eV
- Work function = U-E
- Do not assume speed is 3.00 *10^8
Explain Quantum Tunneling
Using the Schrodinger equation to obtain the particle’s wave function, on sees that the wave function exists on either side of the barrier. This means that there is a probability of finding the particle on the other side of the barrier.
