IB Physics HL Topic 7 & 12

Outline the evidence that supports a nuclear model of the atom.

GEIGER-MARSDEN EXPERIMENT:
•positive alpha particles fired at thin gold leaf
•expected to travel straight through
•some of alpha particles were deflected through huge angles
•numbers being deflected at any given angle agreed with an inverse square law of repulsion from the nucleus
•evidence for electron energy levels comes from emission and absorption spectra
• existence of isotopes provides evidence for neutrons

Outline one limitation of the simple model of the nuclear atom.

• doesn't explain why electrons do not fall into nucleus
•model doesn't take into account isotopes which have varying atomic masses

Describe the emission spectra and absorption spectra.

•when element given enough energy emits light
•light can be analysed by splitting it into its various colours
•if all possible frequencies of light present, called continuous spectrum
• emission spectrum not continuous but contains only few characteristic colours (certain frequencies)
•same particular frequencies absent if continuous spectrum of light is shone through element in gaseous form, called absorption spectrum

Outline evidence for the existence of atomic energy levels.

•electrons can only occupy given energy levels-energy of electron quantized
•energy levels fixed for particular elements and correspond to allowed orbitals
•when electron moves between energy levels it must emit or absorb energy
•energy emitted or absorbed corresponds to difference between two allowed energy levels
•emission and absorption spectrum unique for each element

Describe photons.

•energy emitted or absorbed in "packets' of light called photons
•higher energy photon corresponds to higher frequency (shorter wavelength) of light
ENERGY OF A PHOTON:
E=hf

Describe the interactions in a nucleus.

•nucleons are arranged so that strong nuclear force of attraction overcomes the coulomb force of repulsion between protons in the nucleus.
•nucleons need to be 1.3 femtometers apart for strong nuclear force to causes them to be attracted to each other and be stable
•if distance more strong nuclear force does nothing
•if less it is strongly repulsive instead.

What are A, Z and N?

Nucleon number (A)
Proton number (Z)
Neutron number (N)

Describe coulomb interaction.

like charges i.e. protons repel one another by coulomb interaction

Describe the phenomenon of natural radioactive decay.

•Radioactive decay is a random and spontaneous process which involves unstable nuclei emitting radioactive particles.

Describe the rate of decay.

•The rate of decay decreases exponentially with time
•proportional to the number of atoms in the sample
•INDEPENDENT OF:
→temperature
→pressure
→chemical composition
→initial amount

dN/dt∝-N

Describe the properties of alpha (α) and beta (β) particles and gamma (γ) radiation.

ALPHA:
•emits He nuclei
•He nuclei ionize air by absorbing electrons
•penetrates up to 4cm of air
BETA NEGATIVE
•turns neutron into proton, electron, and anti-neutrino
•daughter particles ionize air by colliding with other electrons
•penetrates up to 1-3m of air
BETA POSITIVE
•turns proton into neutron, positron, and neutrino
•daughter particles ionize air by colliding with other electrons
•penetrates up to 1-3m of air
GAMMA
•emits photons
•photons ionize air by positively charging air molecules
•penetrates up to several mm of Pb

Explain why some nuclei are stable while others are unstable.

•as elements possess more and more nucleons (particularly above 20), more neutrons must be added to counteract the increasing electrostatic repulsion forces caused between protons
•at higher levels, there is more potential to become unstable
•Unstable nuclei emit alpha particles to reach more stable levels

Describe and give an example of an artificial (induced) transmutation.

•causes change in nucleon number
•nucleus is bombarded with a nucleon/s which results in a nuclide with a different nucleon number
•This creates radioactive isotopes of other elements
•bombardment of neutrons may be used to form isotopes of an element

Define the term unified atomic mass unit.

•u
•1/12 of the mass of a carbon-12 atom = 1.66x10⁻²⁷kg

Define the concepts of mass defect, binding energy and binding energy per nucleon.

MASS DEFECT:
difference between the mass of the nucleus and its component nucleons
BINIDING ENERGY:
energy released when a nuclide is assembled from its component nucleons
BINDING ENERGY PER NUCLEON: energy released per nucleon when a nuclide is assembled from its component nucleons
E=mc²
NUCLEAR MASS=atomic mass-mass of electrons

Draw and annotate a graph showing the variation with nucleon number of the binding energy per nucleon.

•in order to compare energy states of different nuclei, calculate binding energy per nucleon
•total binding energy nucleus divided by total number of nucleons
•largest binding energy per nucleon is iron-56 ⁵⁶₂₆Fe

Describe the processes of nuclear fission and nuclear fusion.

NUCLEAR FISSION
•heavier nucleus induced to split into smaller nuclei and releases energy (in the form of KE of daughter nuclei and neutrons) and neutrons which may collide with other nuclei and continue a chain reaction
•e.g. uranium nucleus bombarded with a neutron causing uranium to split into two smaller nuclei
¹₀N + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₂Kr + 3¹₀n + energy
NUCLEAR FUSION
•smaller nuclei combine to form a heavier nucleus
•requires extremely high temperatures and pressure
•energy is released from the KE of the heavier nucleus formed
•no chain reactions
²₁H+³₁H→⁴₂He+¹₀n+energy

What is the main source of the Sun's energy?

Nuclear fusion

Describe the photoelectric effect.

•under certain conditions, when light (UV light) shone onto metal surface (such as zinc), electrons are emitted from surface
•below certain threshold frequency, f₀, no photoelectrons are emitted, no matter how long it is exposed to light
•above threshold frequency, maximum KE of these electrons depends on frequency of incident light
•number of electrons emitted depends on intensity of light and does not depend on frequency
•these observations cannot be reconciled with view that light is a wave, a wave of any frequency should eventually bring enough energy to metal plate.

Describe the concept of the photon, and use it to explain the photoelectric effect.

•light thought as being made up of particles
•electrons on surface need certain minimum energy in order to escape from surface
•minimum energy called work function Φ
•UV light energy arrives in little packets of energy called photons
•energy carried by photons: E=hf
•if energy of photon is large enough, gives electron enough energy to leave surface
•any extra energy would be retained by electron as KE
•if energy of photon is too small, electron will still gain this amount of energy but soon share it with other electrons
hf=Φ+KEmax or hf=Φ+Vse

Describe and explain an experiment to test the Einstein model.

MILLIKANS STOPPING POTENTIAL EXPERIMENT:
SETUP: an evacuated chamber, a voltmeter, an ammeter, and a variable voltage supply connected by a circuit.
HOW IT WORKED:
•photoelectrons emitted by cathode
•they are accelerated across to anod by potential difference
•potential between cathode and anode can be reversed
•in this situation, electrons decellerated
•at certain value, stopping potential, Vs, no more photocurrent is observed
•stopping potential depends on frequency of UV light in the linear
•stopping potential is a measure of max KE of electrons
Max KE of electrons=Vse
[since p.d.=energy/charge and e=charge on an electron]
∴½mv²=Vse ∴v=2Vse/m

Describe the de Broglie hypothesis and the concept of matter waves.

•all moving particles have a "matter wave" associated with them
•all particles can act and travel as waves (wave-particle duality) with a wavelength of λ= ρ/h.

Outline an experiment to verify the de Broglie hypothesis.

DAVISSON-GERMER EXPERIMENT:
•beam of electrons strikes a target nickel crystal
•electrons are scattered from surface creating an electron diffraction pattern
•maximum scattered intensity recorded at an angle with constructive interference
•the wavelengths calculated by the diffraction pattern corresponded with de Broglie's hypothesis.

Outline a laboratory procedure for producing and observing atomic spectra.

shining light through a sample in a spectroscope, an atomic absorption spectra may be observed

Explain how atomic spectra provide evidence for the quantization of energy in atoms.

The spectral lines in atomic emission and absorption spectra show the electrons shifting orbits by either releasing or absorbing discrete amounts of energy and hence, a quantization of energy within atoms.

Outline the Schrödinger model of the hydrogen atom.

•model assumes that electron orbits may be described by wave functions
•The square of the amplitude of the wave function will give the probability of finding the electron at a particular point
•The atomic model consists of a nucleus and an electron cloud
•exact position of electron is not known but can indicate probability of the electron being there
•only few particular energies result in wave functions that fit the boundary conditions

State what is meant by a wave function.

•a function whose absolute squared value may be used to calculate the probability of finding a particle near a given position

Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy.

•identifies fundamental limit to the possible accuracy of any physical measurement
•impossible to measure exactly the position AND momentum of a particle simultaneously
•they are linked variables, called conjugate quantities
•the more precisely the position is determined, the less precisely the momentum is known in this instant and visa versa.
EQUATIONS GIVEN IN DATA BOOK

Relate Heisenberg uncertainty principle to de Broglie hypothesis.

•if a particle has a uniquely defined de Broglie wavelength, then momentum known precisely but all knowledge of postion is lost

Explain how the radii of nuclei may be estimated from charged particle scattering experiments.

•alpha particles bombard gold atoms
•as approach gold nucleus feel force of repulsion
•if alpha particle heading directly for nucleus, will be reflected straight back along same path
•no alpha particle actually collides with nucleus-they do not have enough energy
•alpha particles emitted from source with known energy
•come in and gain electrostatic potential energy and lose KE
•closest approach all energy is potential
since electrostatic energy=q₁q₂/4πE₀r , since we know q₁,q₂, can work out r

Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.

•sample of atoms put into its gaseous state
•bombarded with electrons to leave the remaining nucleus
•accelerated through an electric field
•deflected by a magnetic field
•received by a detector
•mass of the nuclei can then be determined by v = E/B
•if a moving ion enters a constant magnetic field B, folow a circular path where the magnetic force provides the centripital force

Bqv=mv²/r where r is the radius of the circle
•radius of circle will depend on mass of the ion, a larger mass ion will travel in a larger circle

Describe one piece of evidence for the existence of nuclear energy levels.

•when alpha particles or gamma photon is emitted from nucleus only discrete energies are observed
•these energies correspond to the difference between two nuclear energy levels in the same way that the photon energies correspond to the difference between two atomic energy levels
•the different alpha particle energies represent decay of a nucleus to different energy states of a daughter nucleus
•since the energies of the alpha are discreet it means that the energy levels of the daughter nucleus must be discrete
•however beta particles are observed to have continuous spectrum of energies

Describe the β decay, and how it explains the existence of the neutrino.

•the spectrum is continuous with a maximum value of energy
•the resulting energy difference between energy of any β and maximum β energy is accounted for by the energy of the neutrino
•reference to energy difference between parent energy level and excited energy level of daughter

Describe β⁺ decay, including the
existence of the neutrino.

NEUTRINO:
•is virtually undetectable particle
•neutrino (and antineutrino) must be electrically neutral
•mass very small (practically zero)
•carries away excess energy
β⁺ DECAY:
¹₁p→¹₀n+⁰₊₁β⁺+ν
β⁻ DECAY:
³₁H→³₂He+⁰₋₁β⁻+ṽ (antineutrino)

State the radioactive decay law as an exponential function and define the decay constant.

N = N₀e-λt
The decay constant (λ) is the probability of decay of a nucleus per unit time.

Derive the relationship between decay constant and half-life.

N = N₀e^(-λt)
if t=T½
N=N₀/2
N₀/2=N₀e^(-λT½)
½=e^(-λT½)
ln(½)=-λT½
T½=ln2/λ

Outline methods for measuring the half-life of an isotope.

•Shorter half-lives may be measured directly with laboratory equipment.
•Longer half-lives may be calculated theoretically using the radioactive decay law. By initially calculating for λ with λ = A/N, where A is the amount of activity and N is the number of nucleons and then later t = (ln 2)/λ.

Outline the Bohr model of the atom

-A certain number of 'allowed' orbits for an electron
-Electrons do not radiate energy when in a stable, circular orbit
-Orbits quantized in terms of angular momentum

What are some issues with the Bohr model?

-Doesn't account for relative intensity of different spectral lines
-Electrons in circular orbits because they are always accelerating and thus radiating energy. Bohr states that stable electrons will not radiate energy, and that those who do would spiral into the nucleus
-Doesn't say why the energy levels even exist
-Bigger atoms deviate from predictions

How does the Heisenberg uncertainty principle allow tunnelling?

In order for a particle to escape, it would need energy greater than the escape energy. The particle with not enough energy can 'borrow' energy provided it pays it back in a certain amount of time according to the Heisenberg uncertainty principle. Thus, it can escape and then give the energy back.