Quantum, Nuclear and X-rays CT Flashcards
Photoelectric effect
an interaction between a photon and an electron in a metal, in which the electron is removed from the surface of a metal
Photons
a quantum of electromagnetic energy
Unit: electronvolt (eV)
Symbol: γ
Planck constant
a fundamental constant that links the energy of a photon E and its frequency f,
E = hf
Unit: Js
Symbol: h
electronvolt (eV)
the energy gained by an electron travelling through a potential difference of 1 volt
1 eV = 1.60 x 10⁻¹⁹ J
Threshold voltage
the minimum forward bias voltage across a light-emitting diode (LED) when it starts to conduct and emit light
Threshold frequency
the minimum frequency of the incident electromagnetic radiation that would eject electrons from the surface of a metal
Threshold wavelength
the longest wavelength of the incident electromagnetic radiation that would eject electrons from the surface of a metal
Work function of energy
the minimum energy needed by an electron to free itself from the surface of a metal. Work function (together with threshold frequency and threshold wavelength) is a property of the metal.
Dispersion
the technical term for the splitting of light into its components
Continuous spectrum
an emission spectrum that consists of a continuum of wavelengths
Emission line spectrum
a spectrum with bright-coloured lines of unique wavelengths
Absorption line spectrum
a spectrum with dark lines of unique wavelengths seen against the background of a continuous spectrum
Energy levels/states
a quantised energy state of an electron in an atom
Quantised
a quantity is said to be quantised when it has a definite minimum magnitude and always comes in multiples of the magnitude
restricting a variable, observable quantity to discrete values
Transition
term used to describe a jump made by an electron between two energy levels
Ground state
the lowest energy state that can be occupied by an electron in an atom
de Broglie wavelength
the wavelength associated with a moving particle, given by the equation
λ = h/p or λ = h/mv
Mass defect
the difference between the total mass of the individual separate nucleons and the mass of the nucleus
Atomic mass unit
1/12 of the mass of a neutral atom of carbon-12
Symbol: u
Binding energy
the minimum external energy required to completely separate all the neutrons and protons of a nucleus to infinity
Fission
the process in which a massive nucleus splits into two smaller nuclei
Fusion
the process in which two light nuclei join together to form a heavier nucleus
Decay constant
the probability that an individual nucleus will decay per unit time
Unit: s⁻¹
Symbol: λ
Activity
the rate of decay of a nuclei of a radioactive source
Unit: Bq (becquerel)
Symbol: A
Count rate
the number of particles (beta or alpha) or gamma-ray photons detected per unit time by a Geiger–Müller tube
count rate is always a fraction of the activity of a sample
Exponential decay
the decrease of a quantity where the rate of decrease is proportional to the value of the quantity
Half life
the half life t₀.₅ of an isotope is the mean time taken for half of the active nuclei in a sample to decay
Einstein relation (2)
E = hf and E = hc/λ
(E) energy of a photon [J]
(h) Planck’s constant [eV]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(λ) wavelength [m]
Speed of any type of charged particle
v = √2eV/m or v = √2Eᴋ/m
(v) electron speed [ms⁻¹]
(e) electron charge [C]
(V) voltage [V]
(m) mass of particle [kg]
(Eᴋ) kinetic energy [J]
Einstein’s photoelectric equation
E = hc/λ = hf = Φ + 1/2mvₘₐₓ²
(E) energy of a photon [J]
(h) Planck’s constant [eV]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(λ) wavelength [m]
(Φ) work function of the metal [J or eV]
(1/2mvₘₐₓ²) maximum kinetic energy of emitted photoelectron [J]
Equations when incident radiation frequency equals threshold frequency (3)
hf₀ = Φ
∴
f₀ = Φ/h
∴
λ₀ = hc/Φ
(h) Planck’s constant [Js]
(f₀) threshold frequency [Hz]
(Φ) work function [J or eV]
(λ₀) threshold wavelength [m]
(c) wave speed [ms⁻¹]
Momentum of a photon
p = E/c
(p) momentum [kgms⁻¹]
(E) energy of the photon [J]
(c) photon speed [ms⁻¹]
The energy of a photon, absorbed or emitted, as a result of an electron making a transition between two energy levels E₁ and E₂
hf = E₁ - E₂
hc/λ = E₁ - E₂
(h) Planck’s constant [Js]
(f) frequency [Hz]
(c) wave speed [ms⁻¹]
(E) energy levels [J or eV]
de Broglie wavelength equation
λ = h/p
(λ) wavelength [m]
(h) Planck’s constant [Js]
(p) momentum [kgms⁻¹]
Finding wavelength using angle of separation
λ = 2d sinθ
(λ) wavelength [m]
(d) spacing of layers [m]
(θ) angle of diffraction [º]
Einstein’s mass energy equation
E = mc²
(E) energy [J]
(m) mass [kg]
(c) speed of light [ms⁻¹]
Activity (2)
A = (-)λN = ∆N/∆t
(A) activity [Bq]
(λ) decay constant [s⁻¹]
(N) number of undecayed nuclei
(t) time [s]
Radioactive decay formula
A = A₀ e⁻*ᵗ
(A) activity [Bq]
(A₀) activity at time t = 0 [Bq]
(*) decay constant (λ) [s⁻¹]
(t) time [s]
Half-life and decay constant relationship
λ = ln2/t₀.₅
= 0.693 / t₀.₅
(λ) decay constant [s⁻¹]
(t) time [s]
Attenuation of x-rays as they pass through a uniform material
I = I₀ e⁻*ˣ
(I) transmitted intensity [Wm⁻²]
(I₀) initial intensity [Wm⁻²]
(*) attenuation coefficient (µ) [m⁻¹]
(x) thickness of the material [m]
Electronvolt and Joules conversion
To convert from eV to J, multiply by 1.60 x 10⁻¹⁹
To convert from J to eV, divide by 1.60 x 10⁻¹⁹
Observations of photoelectric effect
Textbook table 28.4
Diagrams showing electron dropping to a lower energy level, emitted and absorbed
Textbook figure 28.18 a & b
(emission moving down, absorption moving up)
Wave particle duality of light
Light interacts with matter (eg. electrons) as a particle - The evidence for this is provided by the photoelectric
Light propagates through space as a wave - The evidence for this comes from the diffraction and interference of lights using slits
When electron receives energy of the same magnitude as its ground state value
Electron entirely removed from the nucleus
Basic decays
When an unstable nucleus undergoes radioactive decay the nucleus before the decay is called the parent nucleus and after the decay is called the daughter nucleus
In α decay, the nucleon number decreases by 4 and the proton number decreases by 2
In β⁻ decay, the nucleon number is unchanged and the proton number increases by 1
In β⁺ decay, the nucleon number is unchanged and the proton number decreases by 1
In gamma decay, there is no change in nucleon or proton number
For the emission of an alpha particle use the notation He and for a beta particle use the notation e.
Mass changes according to Einstein’s equation
The mass of a system increases when energy is added to it
The mass of a system decreases when energy is released from it
To calculate mass change add the mass of the decay particle to the daughter nucleus. Subtract the parent nucleus mass from this.
∆m = final mass - initial mass
Stability comparison of different nuclides
In order to compare the stability of different nuclides, we need to consider the binding energy per nucleon.
Determining binding energy per nucleon
Determine the mass defect for the nucleus
Use Einstein’s mass-energy equation to determine the binding energy of the nucleus by multiplying the mass defect by c²
Divide the binding energy of the nucleus by the number of nucleons
Fusion and fission graph of binding energy per nucleon against nucleon number
Textbook figure 29.6
Spontaneous decay
Radioactive decay is both spontaneous and random
Nuclear decay is spontaneous because:
1. the decay of a particular nucleus is not affected by the presence of other nuclei
2. the decay of nuclei cannot be affected by chemical reactions or external factors such as temperature and pressure
Nuclear decay is random because:
1. it is impossible to predict when a particular nucleus in a sample is going to decay
2. each nucleus in a sample has the same chance of decaying per unit time
Aims of radiographers (2)
To reduce the patient’s exposure to harmful x-rays as much as possible
To improve the contrast of the image, so that the different tissues under investigation show up clearly in the image
Types of x-rays used
Bone is a good absorber of radiation hence a hard X-ray is used
Muscle tissue is a poor absorber hence will require a longer exposure using much softer (long-wavelength, low-frequency) X-rays.
X-ray tube diagram
Textbook figure 30.4
