Chapter 3 - Quantum phenomena Flashcards
What is the photoelectric effect?
Electrons are emitted from the surface of a metal when electromagnetic radiation above a certain frequency is directed at the metal
What is the threshold frequency of a metal?
The minimum frequency that the incident electromagnetic radiation must be for electrons to be emitted from the surface
Equation for the maximum value of wavelength for the photoelectric effect to take place
Wavelength of the incident light must be less than a maximum value equal to the speed of light divided by the threshold frequency of the metal
λ = c/f
How does the intensity of the incident radiation effect the electrons emitted?
The number of electrons emitted per second is proportional to the intensity of the incident radiation, provided the frequency is greater than the threshold frequency
What happens if the frequency of the incident radiation is less than the threshold frequency?
No photoelectric emission from the metal surface can take place, no matter how intense the incident radiation is
How quickly does photoelectric emission take place?
Photoelectric emission occurs without delay as soon as the incident radiation is directed at the surface, provided the frequency of the radiation exceeds the threshold frequency and regardless of intensity
Why does the wave theory of light not explain the photoelectric emission
Cannot explain the existence of threshold frequency or why photoelectric emission takes place without delay
- According to the wave theory, each conduction electron at the surface should gain some energy from incoming waves, regardless of how many waves arrive per second (frequency)
Observing the photoelectric effect using a gold-leaf electroscope
- UV radiation from a UV lamp directed at the surface of a zinc plate placed on the cap of a gold leaf electroscope
- Device a very sensitive detector of charge
- When it’s charged, the thin gold leaf of the electroscope rises as it’s repelled from the metal stem as they both have the same charge
What happens if the gold-leaf electroscope is negatively charged
- The leaf rises and stays in position
- If UV light is directed at the zinc plate, the leaf gradually falls
- Photoelectrons at the zinc surface are emitted due to the photoelectric effect when UV light is directed at the surface
- The metal stem loses some negative charge so the leaf is no longer repelled from it
What happens if the gold-leaf electroscope is positively charged?
- The leaf rises and stays in position
- Leaf stays regardless of whether UV light is directed at the zinc surface, as photoelectric emission causes the loss of photoelectrons and negative charge, so has no effect on the positive charge
- Leaf stays repelled as both it and the stem are positively charged
What is Einstein’s photon theory of light?
- Einstein assumed that light is made up of wavepackets called photons
- Used to explain the photoelectric effect
Energy of a photon
E = hf
f = c/λ
E = hc/λ
What happens to electrons at a metal surface when light is directed at it?
When light is incident on a metal surface, an electron at the surface absorbs a single photon from the incident light and gains energy equal to hf, where hf is the energy of the light photon
How is the work function important in the photoelectric effect?
An electron can leave the metal surface if the energy gained from a single photon exceeds the work function, ϕ, of the metal
What is the definition of the work function?
Work function - the minimum photon energy needed for a conduction electron to escape from the metal surface when the metal is at zero potential.
Excess energy gained by the photoelectron becomes its kinetic energy.
Equation for the maximum kinetic energy for an emitted electron
E(kmax) = hf - ϕ
Equation for photon energy using the work function
hf = E(kmax) + ϕ
Emission can take place provided E(kmax) > 0 or hf > ϕ
Equation for threshold frequency
f(min) = ϕ/h
(hf = E(kmax) + ϕ rearranged when E(kmax) = 0)
What is stopping potential?
Stopping Potential, V(s):
- The minimum potential needed to stop photoelectric emission
- Electrons that escape from the metal plate are attracted back to it by giving the plate a sufficient positive charge
How does stopping potential work?
- The maximum kinetic energy of the emitted electron is reduced to zero because each emitted electron must do extra work equal to e x V(s) to leave the metal surface, where e is the charge of an electron
- Therefore maximum kinetic energy is equal to e x V(s)
Why is planck’s constant significant?
The energy of each vibrating atom is quantised - can only take certain values
What are conduction electrons?
Conduction electrons in a metal move about at random.
The average kinetic energy of a conduction electron depends on the temperature of the metal
What happens when a conduction electron absorbs a photon?
- It’s kinetic energy increases by an amount equal to the energy of the photon
- If the energy of the photon exceeds the work function of the metal , the conduction electron can leave the metal
- If the electron does not leave the metal, it collides repeatedly with other electrons and positive ions, and quickly loses its extra kinetic energy
What is a vacuum photocell?
A glass tube containing a photocathode (a metal plate) and a smaller metal anode.
How does a vacuum photocell work?
When light of a frequency greater than the threshold frequency of the metal is directed at the photocathode, electrons are emitted from the cathode and attracted to the anode
What is the microammeter in a circuit with vacuum photocell used for?
- Measures the photoelectric current
- Photoelectric current proportional to the number of electrons that transfer from the cathode to the anode per second.
Equation for the number of electrons that transfer in a vacuum photocell per second
The number of electrons that transfer from the cathode to the anode per second = I/e
- I is the photoelectric current
- e is the charge of an electron
What is light intensity?
- A measure of the energy per second carried by the incident light
- Proportional to the number of photons per second incident on the cathode for a vacuum photocell
- Each photoelectron absorbs one photon to escape the metal surface - the number of photoelectrons emitted per second is proportional to the intensity of the incident light
What is the relationship between light intensity and kinetic energy of the emitted photoelecton?
- The intensity of the incident light does not affect the maximum kinetic energy of the photoelectron.
- No matter how intense the light is, the energy gained by a photoelectron is due to the absorption of one photon only
How is the maximum kinetic energy of the photoelectrons emitted for a given frequency of light measured?
- Measurements for different frequencies plotted as a graph of E(kmax) against f
- Gives a straight line in the form y = mx+c
E(kmax) = hf - ϕ
y = E(k), x = f
gradient = h , y-intercept = -ϕ
x-intercept = threshold frequency (when E(kmax) = y = 0)
What is ionisation?
The process of creating an ion
- Alpha, beta and gamma radiation create ions when they pass through substances and collide with its atoms
- Electrons passing through a flourescent tube create ions when they collide with atoms of the gas or vapour in the tube
How can we measure the energy needed to ionise a gas atom?
By making electrons collide at increasing speeds with gas ina a sealed tube
What is released into the tube?
Electrons emitted from a heated filament in the tube and attracted to a positive metal plate, the anode at the other end of the tube
What happens to the potential difference in the tube?
Potential Difference between the anode and the filament increased to increase the speed of the electrons
What does the ammeter record?
The ammeter records a very small current due to electrons from the filament reaching the anode
When does ionisation occur?
No ionisation occurs until the electrons reach a certain speed, where each arrives near the anode with enough kinetic energy to ionise a gas atom by knocking an electron out of the atom
What does ionisation cause?
Ionisation near the anode causes a much greater current to pass through the ammeter
How is ionisation energy calculated?
Measure Pd when current starts to increase to calculate ionisation energy of the gas atom
- Equal to work done on each electron, and work is transformed to kinetic energy.
Work done = charge, e x tube potential difference, V.
Therefore ionisation energy of a gas atom = eV
Why should the gas in the tube be at low pressure?
Gas needs to be at sufficiently low pressure, otherwise there are too many atoms in the tube and the electrons cannot reach the anode.
What is an electron volt?
Unit of energy equal to work done when an electron is moved through a pd of 1V
- For charge, q, moved through pd, V, work = qv
What is 1 electron volt equal to in joules?
1 eV = 1.6 x 10^-19J
- Electron of charge 1.6 x 10^-19C moved through pd of 1V
What is excitation?
An electron moves from an inner shell to an outer shell
- Energy needed because the atomic electron moves away from the nucleus in the atom
What are the excitation energies of an atom?
- The energy levels at which an atom will absorb energy.
- Only happens at certain energies characteristic of the atom
- Each energy level corresponds to a cell
Why is excitation energy always less than ionisation energy?
- The atomic electron is not removed completely from the atom when excitation occurs
How can the excitation energy of atoms be determined?
- Using a gas-filled tube with a metal grid between the filament and the anode
- Pd increased between filament and anode
- Measure pd when current falls
- Current falls as some energy absorbed from electrons in excitation by collision with electrons in the metal
What is excitation by collision?
Atoms can absorb energy from colliding electrons without being ionised.
Energy used to excite the atomic electrons
What happens to the current if the colliding electron loses all of its kinetic energy?
If the colliding electron loses all its kinetic energy when it causes excitation, the current due to the flow of electrons through the gas is reduced.
What happens if the colliding electron does not have enough energy to cause excitation?
If the colliding electron does not have enough energy to cause excitation, it is deflected by the atom, with no overall loss of kinetic energy
How are electrons in the atom trapped?
Electrons in an atoma are trapped by the electromagnetic force of attraction in the nucleus.
How does the energy of an electron in each shell vary?
- Energy of an electron in a shell is constant
- An electron in a shell near the nucleus has less energy than an electron in a shell further from the nucleus
How many electrons can each shell hold?
- Each shell can only hold a certain number of electrons
- e.g. innermost shell can only hold 2 electrons, next nearest shell can only hold 8
What is the ground state of an atom?
The lowest energy level/shell
How does an atom become to be in an excited state?
- An atom in the ground state absorbs energy
- One of its electrons moves to a shell at a higher energy
- Atom now in an excited state
What is an energy level diagram?
- Shows the allowed energy values/levels of an atom
- Each allowed energy corresponds to a certain electron configuration in the atom
- Ionisation level considered the zero level, not the ground state, to ensure energy levels shown below are negative`
What happens in de-excitation?
- An excited atom moves to a lower energy level
- Electron from an outer shell transfers down to a lower shell with a vacancy following excitation
- Electron emits a photon equal to the energy lost by the electron
Why does de-excitation happen?
- The electron configuration in an excited atom is unstable as the electron that moves to the outer shell leaves a vacancy in the shell it moves from
- Atom absorbs energy in excitation but does not retain it permanently - energy eventually lost through the photon emitted in de-excitation
What path can an electron take in de-excitation?
May de-excite directly to the shell with the vacancy or indirectly via several energy levels if intermediate energy levels are present
Equation for the energy emitted by the photon in de-excitation
Energy of the emitted photon, hf = E1 - E2
- Moves from energy level E1, to lower energy level E2
What is excitation by photons?
An electron in an atom can absorb a photon and move to an outer shell where a vacancy exists
When can excitation by photons happen?
- Only when the energy of the photon is exactly equal to the gain in the electron’s energy
- Energy of the photon must be exactly equal to the difference between the final and initial energy levels of the atom
- If not, it will not be absorbed
Why are some substances flourescent?
- Atoms absorb photons of certain energies from ultraviolet radiation and become excited
- When they de-excite, they emit photons of the same or lesser energies
- When the source of UV radiation is removed, they stop glowing
What is a flourescent tube?
- A glass tube with a flourescent coating on its inner surface
- Tube contains mercury vaopur at low pressure
- When the tube is on, it emits visible light
How does a flourescent tube emit visible light?
_- Filament electrodes heat and release electrons into the tube of low pressure mercury vapour
- Ionisation and excitation of the mercury atoms occur as they collide with each other and with electrons in the tube
- The mercury atoms emit UV photons and visible photons of much less energy when they de-excite
- UV photons are absorbed by the atoms of the flourescent coating, causing excitation of its atoms
- The coating atoms de-excite in steps and emit visible photons
How is a flourescent tube more efficient than a filament lamp?
- A typical 100W lamp releases about 10-15W of light energy, the rest wasted as heat
- A flourescent tube can produce the same light output with no more than a few watts of power wasted as heat
Why is a starter unit needed for a flourescent tube?
- The mains voltage is too small to ionise the vapour in the tube when the electrodes are cold
How does the starter unit of a flourescent tube work?
- Argon gas in the starter switch unit conducts and heats a bimetallic strip, making it bend, so the switch closes
- The current through the starter unit increases enough to heat the filament electrodes
- When the bimetallic switch closes, the gas in the starter unit stops conducting, so the strip cools and opens
- The mains voltage now acts between the two electrodes, which are now hot enough for ionisation of the gas to occur
What is a continuous spectrum of light?
When white light is split into the entire, continous spectrum of visible light
e.g. a rainbow, or a prism splitting a beam from a filament lamp
What happens when a prism is used to split a beam of light from a tube of glowing gas?
A spectrum of discrete lines of different colours can be seen instead of a continuous spectrum
What do the wavelengths of the lines of a line spectrum represent?
- The combination of wavelengths of the lines of a line spectrum for an element are characteristic of the atoms of that element.
- No other element produces the same pattern of light wavelengths
How can an element be identified from a line spectrum?
- By measuring the wavelengths of the lines
Why is each line spectrum unique to that atom?
- The energy levels of each type of atom are unique to that atom
- The photons emitted are characteristic of the atom
How is each line spectrum unique?
- Each line in a line spectrum is due to the light of a certain colour and therefore a certain wavelength
- The photons that produce each line all have the same energy, which is different from the energy of the photons that produce any other line
- Each photon is emitted when an atom de-excites due to one of its electrons moving to an inner shell
How can an element be identified from its line spectrum?
- Find the wavelength of the colour of each line
- For each wavelength, calculate the energy of the photon that produced that line using E = hf = hc/λ
- This energy value represents the difference in the energy levels of an atom
- Given the energy level diagram for the atom, we can identify on the diagram the transition/change in energy that causes a photon of that wavelength to be emitted
What is the dual nature of light?
Light can behave as a wave or as a particle, according to the circumstances
When is the wave-like nature of light observed?
Through diffraction and the interference pattern produced in a double slit experiment
How does diffraction suggest that light is a wave?
- Light spreading out through a slit is a characteristic of a wave - particles travelling in straight lines would either be blocked or pass through unaltered, to produce sharp shadows with no spread.
- Dependence on wavelength - how much a wave spreads out depends on its wavelength relative to the size of the slit - no physical property of a particle would affect how much it spreads out
How does interference and the double slit experiment suggest that light is a wave?
- If light was a particle it would not interfere, but instead produce two clusters on the screen corresponding to the slits
- Fringe patterns can be accurately predicted using mathematical equations which rely on wave properties like phase and wavelength. No equation for the motion of particles can describe the interference patterns observed
When is the particle-like nature of light observed?
The photoelectric effect
How does the threshold frequency of the photoelectric effect suggest that light is a particle?
- According to the classical wave theory, energy depends on the amplitude, not the frequency
- This suggests that higher intensity would provide enough energy for photons to be emitted regardless of frequency, but instead intensity has no effect on the energy of the photoelectrons
How does the instantaneous emission of electrons in the photoelectric effect sugget that light is a particle?
- If light were a continuous wave, there would be a delay while electrons accumulate enough energy from the light wave to be ejected
- Instead each photon interacts with an electron in a one-to-one collision, transferring its energy instantaneously and the electron is emitted immediately
What is the dual nature of matter?
Matter can behave like a wave or like a particle, depending on the circumstances
What is evidence that matter has a particle-like nature?
Electrons in a beam can be deflected by a magnetic field
How do electrons suggest deflected in a magnetic field suggest that matter has particle nature?
- When an electron is emitted into a vacuum, its path is curved when a magnetic field is applied, and it strikes a specific spot on a detector screen
- A wave would have a less predictable path and wouldn’t strike the screen in a single discrete spot
What was the de Broglie hypothesis?
The idea that matter particles also have a dual wave-particle nature, first considered by Louis de Broglie in 1923
What is the de Broglie wavelength?
- The wave-like behaviour of a particle is characterised by its de Broglie wavelength, which depends on the momentum, p, of the particle
de Broglie wavelength, λ = h/p
p = mv so λ = h/mv
How can the de Broglie wavelength be altered?
By changing the velocity of the particle
What is evidence of the de Broglie wavelength and that matter has a particle-like nature?
Throught the diffraction of a beam of electrons
What experiment shows electron diffraction?
- A narrow beam of electrons at constant speed in a vacuum tube is directed at a thin metal foil
- Metals are composed of tiny crystalline regions, or grains. Each grain consists of positive ions arranged in fixed positions in rows of a regular pattern
How are electrons diffracted through the metal foil?
- The rows of metal atoms cause electrons in a beam to be diffracted, like diffraction of a beam of light through a slit
- The electrons are diffracted in certain directions only to form a pattern of rings on a flourescent screen at the end of the tube
- Each ring is due to electrons diffracted by the same amount from grains of different orientations, at the same angle to the incident beam
How is the beam of electrons produced?
- By attracting electrons from a heated filament wire to a positively charged metal plate with a small hole at its centre
- Electrons that pass through the hole form the beam
How can the speed of the electrons be increased?
By increasing the potential difference between the filament and the metal plate
What effect does increasing the speed of the electrons have on the de Broglie wavelength?
- Makes the diffraction rings smaller
- Increase in speed makes the de Broglie wavelength smaller (λ = h/mv), so less diffraction occurs and the rings become smaller
How does the de Broglie wavelength explain the energy levels of an atom?
- The de Broglie wavelength of the electron has to fit the shape and size of the shell
- The circumference of the electrons orbit must be equal to a whole number of de Broglie wavelengths
- Circumference = nλ where n = 1 or 2 or 3, etc.
