Wave Particle Duality and the Quantum Theory

Why are spectral lines for each element unique?

- Spectral lines are produced when electrons within excited atoms drop to lower energy levels and emit photons of energy equal to the energy level difference (1) - Each element has a unique set of electron energy levels determined by the charge in its nucleus and hence the number of electrons it has (1) - Hence the different range of photons given off by each element will be unique to that element and will give a characteristic set of spectral lines (1)

How can electrons become excited?

1. Absorption of a photon with energy exactly equal to the energy level difference 2. Bombardment of an electron with sufficient KE to excite the atom 3. Thermal excitation whereby if the sample of gas is hot enough then atomic collisions may be energetic enough to excite atoms.

How does a radio transmitter work?

1. The radio transmitter converts the signal (e.g. radio announcer's voice, music or stream of data) into an alternating current. 2. When this alternating current flows in the transmission antenna, the electrons in the antenna oscillate backwards and forwards. 3. This oscillation of charges in the antenna produces a corresponding electromagnetic wave that radiates outwards in all directions from the antenna.

Black body radiator

A black body radiator is an ideal body that absorbs and emits all wavelengths of electromagnetic radiation perfectly but never reflects the incident radiation.

Why is the same element capable of absorbing only some of the same wavelengths as it emits?

Absorption spectra results when an electron in the ground state gains energy and transitions to a higher energy level. Emission spectra is the result of electrons moving from a higher energy level to a lower one; including all transitions to the ground state. Therefore any absorption spectra line will be present in the emission spectra.

Continuous spectra

Are emitted from hot solids such as the filament of an incandescent light bulb or hot liquids such as molten iron from a smelter. In black body radiators, a large number of electron transitions are possible such that the full range of wavelengths are produced.

Quanta

Discrete fixed amounts, for example discrete fixed amounts of energy (as opposed to continuously variable). Example light photons are discrete packets of energy.

Each photon (quantisation)

Each photon of light has its own cause and effect. It is not cumulative, completely independent of each other.

Fluorescence

Electron gets excited by UV light and drops back down to ground state in two or more steps, one of which may release a photon of visible light (with less energy than UV)

Why do all photoelectrons emitted from a metal not have the same kinetic energy for a given incident wavelength?

Electrons not on the surface will require more energy to escape the crystal lattice structure. The work function is the minimum energy required, some will require more energy than others so will have less kinetic energy when released.

Dispersion

Light splits when it passes through a prism because the different wavelengths of light are refracted by different amounts.

Quantisation (Max Planck)

Max Planck theorised that that energy (vibrational energy of atoms) was quantised (single units/can only possess specific, discrete values) and could be transmitted and absorbed only in integral multiples of small units of energy. Molecules absorb and emit radiation in discrete packets called photons. To gain energy a molecule absorbs a photon and to lose energy a molecule emits a photon

Shorter wavelength

More energetic, higher frequency, higher penetrating power.

Electromagnetic waves and oscillating charges

Oscillating charges produce electromagnetic waves of the same frequency as the oscillation. Electromagnetic waves cause charges to oscillate at the frequency of the wave.

Diffraction

The bending or spreading of waves when they encounter an obstacle or a gap

Reflection

The change in direction of a waveform at the boundary between two different media, so the wave returns to the medium in which it started.

Path difference

The difference in the distance travelled by each wave from each of the 2 slits to a point P on the screen.

Interference

The effect that happens when two waves travelling through the same space meet The light waves interfere to produce an interference pattern of dark (destructive interference) and light (constructive interference) bands

The photoelectric effect

The emission of electrons from a metal when light shines on the metal. Can be explained using the concept of light quanta. If a photon hits an atom of a certain material, it may be absorbed by an electron of that material. However, if the photon has enough energy, the electron is ejected, or emitted, from the atom. In this way, light energy changes into electrical energy. If wires are attached to a photoemittive material, the electrons can flow along the wire and create a current (photocurrent).

The UV catastrophe

The linear mathematical model suggested that as as you get shorter wavelengths intensity should increase as it is expected that intensity is inversely proportional to wavelength. In reality, the decrease in intensity from UV onwards indicates that energy must be quantised into discrete packets called photons.

Work function

The minimum energy of a photon needed to remove an electron from the surface of the material.

An object appears which when

The object appears white when energy is radiated roughly evenly across different wavelengths of the visible spectrum.

Polorisation

The process by which a transverse wave is made to oscillate in one plane only. For unfiltered electromagnetic waves, the plane of oscillation of the electric field can be in any direction. Only transverse waves whose electric field plane of oscillation matches the orientation of the polarising material can pass through.

What are the dark lines in a spectra from a star?

These dark lines are absorption lines. When light travels through the elements and compounds in stars, photons of certain wavelengths are absorbed. The light from the star when viewed on Earth, therefore, is missing certain wavelengths. This causes the dark lines in the spectrum.

Microwave ovens

Tuned to produce electromagnetic radiation that oscillates at the same frequency as the resonant frequency of water molecules

Why did the double slit experiement lead to a significant change in scientific understanding?

Up until Young's experiment, most scientists supported a particle or 'corpuscular' model of light. Young's experiment demonstrated interference patterns, which are characteristic of waves. This led to scientists abandoning the particle theory and supporting a wave model of light.

Why does a solution of chromium ions for example appear green?

When white light is shone through the solution, the molecules absorb certain frequencies of light. As white light contains all colours of visible light, the green colour is what we perceive to be the combination of all colours in white light without the colours which were absorbed.

Young's double slit experiment

Young's double-slit interference experiment provided evidence to support the wave model of light. According to the particle theory, light should have passed directly through the slits to produce two bright lines or bands on the screen. Instead, Young observed a series of bright and dark bands or 'fringes'. This is because as light is projected onto a screen with 2 small slits, the light waves diffracting through the 2 slits interfere with one another and produce a predictable pattern of alternating light and dark bands on the detector screen.

Electromagnetic radiation/waves

electromagnetic waves are transverse waves made up of mutually perpendicular, oscillating electric and magnetic fields.

How does the photoelectric effect support the particle theory of light?

a. Negligible time delay - The wave model predicts that if the intensity of light is low enough then there will be a measurable delay between initiating the illumination of the metal and the observation of a photocurrent. The actual observation is that regardless of the intensity of the illumination, the photocurrent is observed to flow as soon as the metal is illuminated. b. The existence of a threshold frequency - The wave model predicts that all light, regardless of frequency, should produce a photocurrent since the measure of its energy is its amplitude. The actual observation is that frequencies below a certain value (the threshold frequency) will not produce a photocurrent regardless of the intensity (amplitude) of the wave. c. The independence of stopping voltage from intensity - The wave model predicts that increasing the intensity of the light source will increase the amount of energy delivered to the metal per unit of time. This will result in more photoelectrons being released and a greater range of kinetic energies of the photoelectrons as indicated by an increased stopping voltage. The actual observation is that increasing the intensity increases the photocurrent but has no effect on the stopping voltage. - this one I'm not sure if I can use it

Planck's constant is very small, which indicates that

energy is quantised on an extremely small scale, so the gradations appear to not exist and energy appears continuous.

As temperature increases (black body radiation)

intensity increases overall and the peak intensity shifts to a shorter wavelength (i.e. a greater proportion of photons have higher energies and overall intensity is greater)

The Wave Model of light

light travelling as a wave

At room temperature, the radiation is

mostly infrared so is not visible to the human eye

not an ideal black body if

not an ideal black body if it does not emit all wavelengths. objects are almost never perfect black bodies but many can be approximated as ideal (e.g. stars)

The perceived colour shifts from

red to yellow to white to blue

Planck's equation

the energy of a photon is proportional to its frequency. This equation allowed for the accurate prediction of the true distribution of black body radiation at all wavelengths.

Transverse waves

waves which oscillate perpendicular to the direction of propagation.

Most of the electromagnetic radiation emitted by the sun is

within the visible spectrum

The de Broglie wavelength

λ=h/mv - the wavelength is associated with the momentum. (note that a photon can have momentum)