Chapter 3 - Quantum phenomena (3.4 - Energy levels in atoms (Fluoresence…
Chapter 3 - Quantum phenomena
3.6 - Wave-particle duality
Evidence for de Broglie's hypothesis
A narrow beam of electrons in a vacuum tube is directed at a metal foil. A metal is composed of many tiny crystalline regions. Each region consists of positive ions arranged in fixed positions in rows in a regular pattern. The rows of atoms cause the electrons in the beam to be diffracted, just as a beam of light diffracted when it passes through light.
The electrons in the beam pass through the metal foil and are diffracted in certain directions only. They form a pattern of rings on a fluorescent 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.
The beam of electrons is produced by attracting electrons from a heated filament wire to a positively charged metal plate, which has a small hole at its centre. Electrons that pass through the hole form a beam. The speed of these electrons can be increased by increasing the potential difference between the filament and the metal plate. This makes the diffraction rings smaller, because the increase of speed makes the de Broglie wavelength smaller. So less diffraction occurs and the rings become smaller.
The wave like behaviour of a matter particle is characterised by a wavelength called its de Broglie wavelength.
Its de Broglie wavelength = h/mv
Perhaps particles of matter also have a dual-wave particle nature, electrons in a beam can be deflected by a magnetic field. This is evidence that electrons have a particle-like nature.
The dual nature of light
is observed, for example, in the photoelectric effect. When light is directed at a metal surface and an electron at the surface absorbs a photon of frequency f, the kinetic energy of the electron is increased from negligible value by hf. The electron can escape if the energy it gains from a photon exceeds the work function of the metal.
is observed when diffraction of light takes place. This happens, for example, when light passes through narrow slit. The light emerging from the slit spreads out in the same way as water waves spread out after passing through a gap. The narrower the gap or the longer the wavelength, the greater the amount of diffraction.
3.5 - Energy levels and spectra
Each line in a lie spectrum is due to 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 if 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,
If the electron moves from energy level E1 to a lower energy level E2
The energy of the emitted photon hf = E1 - E2
The wavelengths of the lines of a line spectrum of an element are characteristic of the atoms of that element. By measuring the wavelengths of a line spectrum, we can therefore identify the element that produced the light.
No other element produces the same pattern of light wavelengths. This is because the energy levels of each type of atom are unique to that atom. So the photons emitted are characteristic of the atom.
A rainbow is a natural display of the colours of the spectrum of sunlight. Raindrops split sunlight into a continuous spectrum
3.4 - Energy levels in atoms
The fluorescent tube is a glass tube with a fluorescent coating on its inner surface. This tube contains mercury vapour at low pressure.
When the tube is on, it emits visible light because ionisation and excitation of the mercury atoms occur as they collide with each other and with electrons in the tube
The mercury atom emit ultraviolet photons, as well as visible photons and photons of much less energy, when they de-excite.
The ultraviolet photons are absorbed by the atoms of the fluorescent coating, causing excitation of the atoms
The coating atoms de-excite in steps and emit visible photons
An atom in an excited state can de-excite directly or indirectly to the ground state, regardless of how the excitation took place
Excitation using photons
An electron in an atom can absorb a photon and move to an outer shell where a vacancy exists, but only if the energy of the photon is exactly equal to the difference between the final and initial energy levels of the atom, otherwise it will not be absorbed by the electron
The electron configuration in an excited atom is unstable because an electron that moves to an outer shell leaves a vacancy in the shell it moves from. Sooner or later, the vacancy is filled by an electron from an outer shell transferring to it. When this happens, the electron emits a photon.
When an electron moves from energy level E1 to a lower energy level E2, the energy of the emitted photon hf = E1 - E2
Electrons in atoms
The lowest energy of an atom is called its ground state. When an atom in the ground state absorbs energy, one its electrons moves to a shell at higher energy, so the atom is now in an excited state.
3.3 - Collisions of electrons with atoms
Excitation by collision
When excitation occurs, the colliding electron makes an electron inside the atom move from an inner shell to an outer shell. Energy is needed for this process, because the atomic electron moves away from the nucleus of the atom. The excitation energy of an atom is always less than the ionisation energy of the atom, because the atomic electron is not removed completely from the atom when excitation occurs
The energy values at which an atom absorbs energy are known as its excitation energies. We can determine the excitation energies of the atoms on the gas-filled tube by increasing the pd between the filament and the anode and measuring the pd when the anode current falls.
Using gas-filled tubes with a metal grid between the filament and the anode, we can show that gas atoms can absorb energy from colliding electrons without being ionised.
If the colliding electron does not have enough kinetic energy to cause excitation , it is deflected by the atom, with no overall loss of kinetic energy.
If a colliding electron loses all its kinetic energy when it causes excitation, the current due to the flow of electrons through the gas is reduced.
The electron volt
For a charge q moved through a pd V, the work done = qV. Therefore, the work done when an electron moves through a pd of 1V is equal to 1.6x10.-19.
The electron volt is a unit of energy equal to the work done when an electron is moved through a pd of 1V
An ion is a charged atom. The number of electrons in an ion is not equal to the number of protons. An ion is formed from an uncharged atom by adding or removing electrons from the atom. Adding electrons makes the atom into a negative ion and vice versa. Any process of creating ions is called ionisation.
3.2 - More about photoelectricity
The vacuum photocell
If measurements for different frequencies are plotted as a graph of E.kmax against f, a straight line graph of y=mx +c where y=E.k, m=h, x=f and c= - work function
The maximum kinetic energy of the photoelectrons emitted for a given frequency of light can be measured using a photocell.
The intensity of the incident light does not affect the maximum kinetic energy of a photoelectron, no matter how intense the incident light is, the energy gained by the photoelectron is due to the absorption of one photon only.
The photoelectric current is proportional to the intensity of the light incident on the cathode. The light intensity is a measure of the energy per second carried by the incident light, which is proportional to the number of photons per second incident on the cathode.
For a photoelectric current I, the number of photoelectrons per second that transfer from the cathode to the anode = I/e where e is the charge of the electron
A vacuum photocell is a glass tube that contains a metal plate, referred to as the photocathode, and a smaller metal electrode referred to as the anode. When light of a frequency greater than the threshold frequency for the metal is directed at the photocathode, electrons are emitted from the cathode and are attracted to the anode. The microammeter in the circuit can be used to measure the photoelectric current.
3.1 - The photoelectric effect
Electrons that escape from the metal plate can be attracted back to it by giving the plate a sufficient positive charge. The minimum potential needed to stop photoelectric emission is called the
stopping potential Vs
. At this potential, the maximum kinetic energy of the emitted electron is reduced to zero because each emitted electron must do extra work equal to e x Vs to leave the metal surface. Hence its
maximum kinetic energy is equal to e x Vs
Einstein's explanation of the photoelectric effect
The maximum kinetic energy of an emitted electron is therefore,
E.kmax=hf - work function
of a metal is the minimum energy needed by an electron to escape from the metal surface, excess energy gained by the photoelectron becomes its
Energy of a photon = hf
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.
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
Photoelectric emission of electrons from a metal surface does not take place if the frequency of the incident electromagnetic radiation is below a certain value known as the
The discovery of the photoelectric effect
Further investigations on the effect of electromagnetic radiation on metals showed that electrons are emitted from the surface of a metal when electromagnetic radiation above a certain frequency was directed at the metal, which is known as the photoelectric effect.