Quanta to Quarks Flashcards
Bohrs model of the atom?
-Significance of the hydrogen spectrum in its development?
Bohrs Model:
Same as Rutherford’s model except:
electron shells- specific locations away from the nucleus where electrons must reside.
At quantum number (n)=1
- closest to nucleus
- big gap to n=2
- lowest energy shell
At n=infinity
- furthest from nucleus
- tiny difference to next shell (continuum)
- highest energy shell
Significance of the Hydrogen Spectrum:
At room temperature, the electron in hydrogen possesses a specific amount of energy at each quantum level. When it undergoes a change in quantum state, it releases energy as EM radiation. The amount of energy depends on the amount of shift in quantum state (change in E=E=hf), thus greater frequency too.
Hence, by analysing the emission spectrum of hydrogen, the arrangement of electrons in the atom could be identified. This gave rise to Bohr’s model.
Since hydrogen showed more than one spectral line, it indicated that the electron existed in multiple energy levels not just one.
Bohr’s Postulates:
1) Stationary States
Atomic electrons orbit the nucleus in special stationary states during which they are stable and do not emit EM radiation.
2) Photoemission due to Electron Transition
Photons of EM radiation emitted when electrons transition from higher to lower energy electron shells
i.e.🔼E=E=hf
Where-🔼E=energy difference between initial and final electron shells
3) Quantisation of Angular Momentum
Electrons are confined to orbiting only at fixed radii from the nucleus because their angular momentum is quantised in units of h/2pi
I.e. Angular momentum of electrons = n x h/2pi
Plancks Contribution to the Concept of Quantised Energy:
- recognised that the energy of oscillating electrons exists in discrete amounts which are multiples of hf
- recognised that emissions or absorptions of energy were die to jumps between energy levels. Unit of energy emitted or absorbed is a quanta
I.e. Resolved apparent contradictions in classical physics and the “ultraviolet catastrophe”
Describe how Bohr’s postulates led to the development of Rydberg’s equation
By combining the expression for the energies of the stationary states with Bohr’s second postulate (🔼E=E=hf), an expression for the energy difference between stationary states can be derived. Hence the energies of the photon that may be emitted or absorbed by hydrogen could be calculated (ionisation energy)
Discuss the limitations of Bohr’s model:
1) Stationary States
could not explain why electrons existed in stationary states, why these states had particular locations and why electrons do not emit EM radiation in them.
-this is because Bohr’s model still viewed electrons as accelerating, quantum physics nature had not been discovered
2) Intensity of Spectral Lines Varies
Could not explain why some spectral lines had a greater intensity than others.
-because some transitions between electron shells were favoured more than others, needs quantum probabilistic rules
3) Hyperfine
Could not explain that some spectral lines, which at first appeared to be one line, were in fact many fine lines spaced very close together
-because he did not know about quantum spin
4)Zeeman Effect
When the hydrogen discharge tube is operating near a magnetic field the each spectral line splits up into several separate lines. Aspect of the phenomenon called the Anomalous Zeeman Effect could not be explained by Bohr.
-requires knowledge of quantum spin, changing their orbits and thus effecting their energy
5) Spectral Lines if Atoms with More than One Electron
Could not predict spectral lines of atoms with more than one electron.
-because more than one electron interact with one another and with the nucleus
Rutherford’s Model of the Atom:
-experimental reasoning
-Progressed from Thomson’s Plum Pudding Model
Alpha particles were fired at thin gold foil, with radial detector (phosphor screen) on other side
Expectation was little to no deflection but 1/8000 deflected back at an angle greater than 90 degrees.
(Had to be some areas of highly dense positive charge for that)
Rutherford’s Model:
- All of the +ve charge and almost all of the atoms mass concentrated at its nucleus
- Electrons orbit the nucleus, attracted by electrostatic force
- most of the atom consists of empty space
Limitations:
1) Orbiting electrons would be an example of an accelerating electric charge. Accelerating charges emit EM radiation, therefore would be constantly emitting EM radiation, the loss of energy causing the electron to spiral into the nucleus.
2) fails to explain spectral lines produced by gases in discharge tubes
- why only emit a specific wavelength?
- why do different gases emit different wavelengths?
Experiment to prove:
Alpha particles fired at thin gold foil with phosphorus screen behind. Expected to pass straight through with little to no deflection.
Actually occasionally an alpha particle would deflect at an angle greater than 90degrees.
Suggested all +ve charge and pass of an atom in a concentrated region i.e. Nucleus.
Prac: To observe spectral emission lines produced by a hydrogen discharge tube
Setup: DC power supply and induction coil hooked up to hydrogen discharge tube (like cathode ray tube) then observe the tune with a spectrometer.
Results: Balmer Series Observed:
- bright red line (650nm)
- blue-green line (480nm)
- blue line (430nm)
- dim violet line (410nm)
Process and present diagrammatic information to illustrate Bohr’s explanation of the balmer series
(Check diagram, basically bohr’s model of the atom with lines from n=3, n=4, n=5 and n=6, all to n=2.
Using bohr’s model and second postulate (used to create rydberg equation) the wavelengths present in the balmer series can be explained by the energy of electrons jump down shells.
de Broglie’s standing wave model of the atom:
- hypothesis?
- equation?
- impact?
hypothesis:
Since waves can have particle-like properties (in case of light) then matter can also behave like waves (matter waves).
equation:
equating E=mc^2 and E=(hc)/lamda
lamda = h/(mv) = h/p
(on formula sheet)
impact:
- initially rejected due to lack of experimental evidence
- Confirmed by Davisson and Germer
- thereafter De Broglie’s Electron Standing Wave Model of the atom adopted because it explains the limitations of Bohr’ model:
- Atomic electrons do not emit EM radiation in ‘stationary states’ because they are manifesting their wave nature.
- Atomic electrons orbit at specific distances from the nucleus because this is where they have a circumference which can fit a whole number of electron wavelengths.
Therefore model of the atom is the same as But at n=1 the circumference of the orbit is enough for one wavelength, at n=2 there is enough room for 2 wavelengths and so on.
Define diffraction?
What happens when 2 waves overlap?
Diffraction: When a wave passes through a narrow slit the wave spreads out. The more similar the wavelength of the wave is to the size of the gap the stronger the diffraction effect.
When 2 waves overlap they create an interference pattern of constructive (where the wave intensity is strengthened) and destructive interference (where the waves cancel each other out.
Constructive peaks are strongest in the middle (in line with the split) and get weaker the further away from the centre they are.
Davisson and Germer’s Experiment:
How did it confirm de Broglie’s proposal?
Aim: To test de Broglie’s matter wave hypothesis.
Method:
1) diagram
Everything is inside a vacuum chamber.
Electron gun (power supply, induction coil, heating element, cathode and anode) fires electrons at a nickel crystal where they deflect to an electron detector which can be moved in a circular arc to check different angles.
2) Use interference pattern and Bragg’s Law (n lamda = 2dsin(theta) ) to find the wavelength of the electrons. Interference patterns are a result of diffusion (i.e. a wave property) and thus if electrons diffract as they move between the spaces in the crystal lattice (think Bragg’s experiment) then they have wave properties.
3) Use de Broglie’s matter have equation (lamda = h/mv = h/p ) to find electron wavelength. Velocity is known from the voltage of the electron gun.
Results:
1) Interference patterns observed confirming electrons have a wave property. Seen as unpredicted peaks in Number of Electrons Detected vs Scattering Angle hich could only be constructive interference.
(graph of exponential curve down with sudden peak)
2) Wavelength predicted by de Broglie’s equation matches the wavelength calculated by Bragg’s law.
Heisenberg’s Contribution to Atomic Theory
1) Heisenberg’s Uncertainty Principle: The product of the uncertainty of position and uncertainty of momentum of a particle is never smaller than h/(4pi)
i. e. (uncertainty of x)(uncertainty of p) >or equal to h/(4pi)
-implies the more we know about position the less we know about momentum and vice versa. If we know with certainty the position of the particle (i.e. (triangle)x = 0) then uncertainty of p approaches infinity.
-only applies in tiny scales in the order of planck’s constant
there is also an uncertainty relationship between energy and time.
The implication of this model to the atom is that the position and momentum of an orbiting electron cannot both be precisely known at the same time i.e. its trajectory is smeared out in space,. as described by the Electron Cloud Model of the atom. (Shows a particle demonstrating its wave nature cannot have a well defines position)
2) Developed a complete model of quantum mechanics using a mathematical approach called matrix mechanics.
Pauli’s Contribution to Atomic Theory
1) Correctly predicted that 4 quantum numbers, each with their own set of rules, must exist to fully describe atomic electrons. At the time there was only 3 known
- n = electron shell
- l = angular momentum
- m = magnetic
and paulis 4th quantm number:
- s = spin
2) Pauli’s Exclusion Principle: No 2 electrons in the same atom can have the same 4 quantum numbers.
This rule in conjuncture with the 4 quantum numbers and their sets of rules to account for the electron configuration of all atoms i.e. the number of electrons that can be in each electron shell).
3) Predicted the existence of neutrinos, produced during radioactive decay
Chadwick’s Discovery of the Neutron:
method:
radioisotopes –(alpha particle)–> beryllium foil –unknown radiation (neutrons)–> paraffin wax –protons–>detector (ionisation chamber)
Equation: (4/2)He + (9/4)Be –> (12/6)C + (1/0)n
french scientists though it would be gamma radiation emitted e.g. (4/2)He + (9/4)Be –> (13/6)C + gamma
1) Chadwick calculated the energy and momentum available for the unknown radiation based on the gamma ray and neutral particle hypotheses by knowing the energy associated with the mass defect in each situation using E=mc^2
2) Chadwick calculated the kinetic energy and momentum of the ejected protons. This required replacing the paraffin wax with nitrogen gas and measuring the recoil of the nitrogen atoms as they emitted protons.
3) Having calculated initial and final energies and momenta Chadwick checked whether the gamma ray hypothesis and the neutral particle hypothesis satisfied the Law of Conservation of Energy and the Law of Conservation of Momentum.
Results:
Only the neutral particle hypothesis satisfied both laws, thus this was the discovery of the neutron.
n.b. the conservation laws were important to Chadwick’s discovery of the neutron as they allowed him to test the validity of the gamma ray and neutral particle hypotheses by knowing the initial and final energies and momenta associated with both.
How did Rutherford predict the existence of the neutron?
discrepancy between number of protons in an atom and its measured mass (i.e. between its atomic and mass numbers). Rutherford hypothesised that a neutral particle of similar mass to the proton must be present in the atom to increase mass without changing charge balance.
Neutron Scattering (Diffraction): Properties and Applications?
1) No electric charge
Usefulness: penetrate deep into the atom, scattering off nucleus rather than being repelled by electrons or protons.
Applications: Research into the properties of atomic nucleus.
2) de Broglie wavelength is close to the size of the spaces between atoms.
Usefulness: Neutrons can produce interference patterns.
Application: Research into the arrangement of atoms in a crystal.
3)Kinetic Energy
Usefulness: Neutron’s trajectory is affected by lattice vibrations
Application: Research into the thermal properties of materials.
4) Magnetic Properties (due to spin)
Application: Research into magnetic properties of materials.
Evaluate the relative contributions of
electrostatic and gravitational forces
between nucleons:
gravitational force attracting nucleons approx = 1.8 x 10^-34 (i.e. really small)
Electrostatic force repelling protons from one another approx = 231N (i.e. pretty damn high)
-no electrostatic repulsion between neutrons or proton-neutron because neutrons have no charge.
Conclusion:
This shows that there must be a very strong attractive force acting in the nucleus (Strong nuclear force)
Strong Nuclear Force Properties:
Very Strong:
Far more influence than electrostatic and much much more than gravitational
Very Short Range:
only extends as far as neighbouring nucleons in the nucleus.
Acts Equally on All Nucleons:
proton-proton, proton-neutron, neutron-neutron
Changes from Repulsive to Attractive:
Locks the nucleons at a tiny distance from one another.
Graph:
- Shows Repulsiveness vs Distance between Nucleons (x10^-15m)
(i. e.-ve on y axis = attractive force) - at distance = 0 repulsiveness = infinity
- at x= 1/2, repulsiveness=0 (i.e. no force)
- attractiveness peaks at just past x=1
- attractiveness decreases at an decreasing rate but at around x=3, force=0
Mass Defect and Binding Energy:
Mass defect = the missing mass when a system moves from a higher to lower energy state.
- Every nucleus has a mass defect as the mass of a nucleus is less than the sum of the protons and neutrons that form it (i.e. the nucleus is a more stable state for them than being free particles)
- change in mass = mass of nucleus - mass of protons and neutrons separately (-ve answer indicates the conversion of mass to energy)
Binding Energy = the energy equivalent of the mass defect of a nucleus
i. e. BE = (change in mass)c^2
- (mass defect must be in kg for this to work)
Binding energy can also be thought of as ‘unbinding energy,’ the amount of energy that would need to be applied to break up a nucleus.
N.B.
Mass Numbers on the periodic table are given in ATOMIC MASS UNITS (u or amu).
-conversion rate is on formula sheet
-There is also a second equation to convert from mass to energy like E=mc^2 for converting from atomic mass to electron volts, also on formula sheet.
Types of Radioactive Decay:
- symbol
- identification of radiation
- reason for decay
- ionisation ability
- penetration power
- level of danger
Alpha Radiation:
Symbol- (4/2)(alpha)
Identification- helium nucleus
Reason for Decay- nucleus is too large therefore unstable
Ionisation Ability- High (+2 charge, large mass and moves slowly i.e. more time for ionisation)
Penetration Power- Low, blocked by paper (quickly loses KE due to many ionisation events)
Danger- Low (unless ingested)
Beta Radiation:
Symbol- (0/-1)(Beta)
Identification- High speed electron
Reason for Decay- nucleus is unstable due to neutron to proton ratio
Ionisation Ability- Moderate
Penetration Power- Moderate, blocked by few mm of aluminium
Danger- Moderate
Gamma Radiation:
Symbol- (0/0)(Gamma)
Identification- High energy photon (EM radiation)
Reason for Decay- nucleus is in excited state, emits energy as gamma ray to return to ground state.
Ionisation Ability- Very Low (can only ionise one atom)
Penetration Power- Very High, blocked by few cm of lead (rarely interacts with atoms)
Danger- High
N.B. In a magnetic or electric field:
- alpha particle will bend as its +2 charge dictates
- beta particle will bend far more than alpha particle as even though it is only a -1 carge (half that of alpha) it is much, much less massive
- gamma radiation will be unaffected
Wilson Cloud Chamber:
(Look at diagram)
Includes: insulated base, dry ice, super-saturated alcohol vapour, felt tips soaked in alcohol, plastic lid,
Strontium-90 (alpha emitter)
Americium-241 (beta emitter)
How it works:
1) Dry ice cools the container so that the alcohol vapour is super saturated, meaning any disturbance in the chamber will cause the alcohol vapour to condense into liquid, forming a condensation trail.
2) Radiation emitted by radioisotopes cause ionisation of atoms which causes condensation trail.
Alpha, beta and gamma
radiation can be detected and the path can be observed by observing the ionisation of the vapour
that is caused by the radiation.
Alpha source:
- short, dense condensation trails
- large number of atoms ionised
- low penetration power
Beta source:
- long, faint condensation trails
- moderate number of atoms ionised
- moderate penetration power
Gamma source:
-Rarely produces an condensation trails in a cloud chamber due to extremely high penetration power and the fact each photon can only ionise one atom.
What is transmutation?
Which types of radioactivity cause natural transmutation?
Transmutation is changing the nucleus from one type (1 element) to another.
Natural transmutation- nucleus that changes identity spontaneously.
Occurs during natural alpha or beta decay but not gamma.
Artificial Transmutation- nucleus changes identity as the result of being bombarded by particles (artificial radioactive decay like in fermi’s experiment)
Development of the model of the atom:
Thomson- discovers electron
- plum pudding model
Rutherford- planetary model
(Also discovers proton but non-assessable)
Bohr- electron shell model
De Broglie- electron standing wave model
Davisson and Germer -electron diffraction experiment
Heisenberg- uncertainty principle
Pauli- exclusion principle
Chadwick- discovers neutron
Uncontrolled vs Controlled Chain Nuclear Reactions:
Uncontrolled:
Each fission event results in more than 1 subsequent fission event (super-critical).
-results in exponential increase in the rate at which energy is released
Application: Atomic Bombs
Requirements:
Fissile Matter- nuclei that easily undergo fission after absorbing a neutron.
Critical Mass- minimum amount of fissile material to support chain reaction
-for atomic bombs there is often a method of bringing together 2 subcritical masses to produce a super-critical mass
Controlled:
Each nuclear fission event results in exactly 1 subsequent fission event (critical)
-Results in a constant rate at which energy is released
Application: Nuclear reactor in nuclear power station
Requirements:
Fissile Matter
Critical Mass
Moderator- which slows down neutrons so that they will be absorbed and cause fission e.g. Heavy water or graphite
Control Rods- capture excess neutrons. Begin fully inserted and removed are raised out of reactor to allow chain reaction to occur. In emergencies they are dropped back in. E.g. Cadmium or boron rods
