Lecture 2: Photoelectric Effect & Compton Scattering Flashcards
photoelectric effect first discovered when observed that
ultraviolet light affected the voltage at which sparking occurred between metal electrodes.
set up to introduce for explaining photoelectric effect
a vacuum chamber containing a metallic plate (it can be of different materials, e.g. sodium) hit by radiation at a certain wavelength and intensity, and a collector on the opposite side. Both sides are connected to a battery that can apply a voltage difference, and the collector is connected to an ammeter that measures the current of the charged particles hitting the collector.
classical expectation of photoelectric effect
The expectation is therefore that the energy of an electron emitted does not depend on the frequency of the light, but on its intensity.
simulated experiment: changing the material and the wavelength
nothing happens until wavelength reaches a certain threshold where electrons start being emitted
below threshold freq, do not see emitted e- even if intensity is adjusted
changing the material changes the critical frequency
e- have more kinetic energy when at a lower wavelength (higher freq)
simulated experiment: changing the intensity and voltage
+ve voltage: e- moving faster and system reaches a saturation current
-ve voltage: higher proportions of electrons start travelling towards the collector but come back, as now the potential is opposed to the initial motion of the electrons.
egardless of light intensity, we can eventually reduce the photocurrent to 0 with a negative stopping voltage v0
the stopping voltage decreases linearly with
the light frequency until it reaches 0
there is no photocurrent below a threshold frequency
why we need a quantum explanation
Classical physics does not explain why no photocurrent is recorded above the threshold wavelength: it should depend on the amplitude and therefore on the intensity, according to classical waves physics.
Electrons are emitted when a work of at least the
binding energy Eb is paid to free them: this value depends on the material of the metallic plate
the minimum work that needs to be done to emit electrons is related to the kinetic energy of the electrons
Eb = hv -W
minimum threshold frequency necessary to eject electrons is
vth = w/h
extra energy ontop of binding energy
kinetic energy which determines a maximum possible velocity
The intensity determines the number of
photons present in the light sent to the metallic plate, so higher intensity means that more electron can be extracted, if the frequency is above the threshold, and the photocurrent increases
The voltage can be tuned to increase the photocurrent by
facilitating the motion of electrons incresing the voltage. A negative voltage can otherwise invert the motion of the electrons, and consequently reduce the photocurrent all the way to zero
problem with plum pudding
According to classical physics, electrons in orbits (accelerating charges) should emit radiation and therefore lose energy and spiral in to the nucleus. What does prevent this from happening? Classical physics could not provide a valid reason.
bohr’s postulates
- e- move in circular orbits determined by Newton and Coulomb’s laws
- orbits are quantised, e- can only occupt stable orbtis
3.e- must emit/absorb energy to move orbits - atomic angular momentum is quantised
Why did the quantum and classical results agree in atoms with large mass number? And why is angular momentum quantized?
Because in large systems classical physics is a good approximation of quantum physics! This is the correspondence principle
Bohr’s correspondence principle
Predictions of quantum theory must correspond to the predictions of classical physics in the region of sizes where classical theory is “known to hold”.
Quantum systems are usually described by quantum numbers
n, and the classical limit should be recovered from the quantum results, for n approaching infinity
problems with Bohr’s model
-failed to predict observed intensities of spectral lines
-good for one-electron atoms but limiting for multi-electron
-could not really explain wave-particle duality
What happens if electrons interact with light at high frequencies such as X-ray?
reasonable to consider the electrons free, since the binding energy of the atom is very small compared to the X-ray energy, so the interaction between the high-frequency radiation and the electron would result in scattering.
Classical expectation: when the EM wave is scattered off atoms, the wavelength of scattered radiation should be
the same as the wavelength of the incident radiation
Based on Thomson’s theory (Thomson’s scattering), the oscillating electric field of the incident radiation would make the electrons of the target atoms
vibrate with the same frequency, and these would radiate electromagnetic waves at the same frequency.
compton found that
with increasing scattering angle, a second peak was appearing at longer wavelength compared to the one of the incident light
This change in wavelength between the peaks of the incoming beam and the scattered one is
the compton shift
compton wavelength of the electron
constant in equation
h/mec
The wave-like and particle-like properties of light can be related by following equation for the momentum p of the photon,
p=kbar k = hv/c = h/lambda
de broglie wavelength
lambda dB = h/p
can also use p=hbar k
where k is the de broglie wavenumber
The idea of de Broglie gives a
qualitative explanation to Bohr’s idea of quantized orbits, as the waves associated to the electrons would interfer, leaving areas of destructive interference where “electrons are forbidden”, while only standing waves would be allowed to “fit” in the Bohr’s circular orbits.
standing wvaes allowed to fit in bohr circular orbits would be given by a
discrete set of wavelengths that interfer constructively if an integral number of wavelengths fits exactly into the circumference of the orbit
n lambda = 2 pi r (r=radius)
The reality is that the Bohr’s model, even with the de Broglie interpretation, still doesn’t capture
he probabilistic nature of quantum physics.
why classical physics is deterministic:
given a system, if you have enough information about it and know the physics to describe its dynamics, you can determine what will happen next to said system
the process of observing a classical system does not affect the final configuration
why quantum physics is probabilistic (electron)
e- is also wavefunction - a probability distribution indicating the regions where the electron is more likely to b
The region of space around the nucleus where there is a high probability of observing the electron (~90-95%) is called
an orbital
‘forbidden’ regions around the nucleus are
the nodes
Electron orbitals introduced by Schrödinger are characterised by
quantum numbers
principle quantum number
n
Indicates the energy level and relative size of the orbital. It can take positive integer values (1, 2, 3, …).
Orbital Angular Momentum Quantum Number (l):
Defines the shape of the orbital and can take values from 0 to n-1 for each value of n. Each value of l corresponds to a specific type of orbital (s, p, d, f…).
magnetic quantum number
ml
Describes the orientation of the orbital in space and can take integer values from -l to +l, including 0
spin quantum number s
for an electron, the spin is 1/2
spin magnetic quantum number ms
specifies the electron’s spin direction which can be either + or- 1/2
