8.1 radioactivity

Created by

Cards (63)

Rutherford experiment
Rutherford scattering
1909 rutherford and marsden fired a beam of alpha particles at thin gold foil
Circular detector screen surrounded foil and alpha source to detect deflected particles
Expected positive particles would be deflected by electrons by small amount
Considerations
In evacuated chamber (vacuum) so alpha particles dont collide with air particles
Thin gold foil used so fewer particles to interact with
All alpha particles has some KE as different velocities would travel at different angles
Used a narrow beam so deflection is more obvious
Result: conclusion
Most alpha particles went straight through the foil
Most of the atom must be empty space
Small number were deflected at large angles
Concentration of positive charge in the atom, like charges repel so positive particles were repelled by positive particles
Very small number came straight back - 1 in 10 000
Positive charge and mass concentrated in a tiny volume in the atom
Fast alpha particles deflected by nucleus
Most of the mass concentrated in the nucleus
Change in atomic structure
5th century BC, Democritus
Proposed all matter made up of identical lumps called atoms
1804, John Dalton
Hypothesis that these tiny spheres couldn't be broken up
Believed each element was made up of a different type of atom
20th century, J.J Thompson
Electrons could be removed from atoms
Dalton’s theory wasn't quite right
Suggested atoms were spheres of positive charge with tiny negative electrons
Plum pudding model
20th century, Rutherford
Suggested atoms didn't have uniformly distributed charge and density
Types of radiation
alpha
helium nucleus
+2 charge
relative mass 4
strongly ionising
slow speed
stopped by paper or a few cm of air
affected by magnetic field
beta -
electron
-1 charge
negligible relative mass
weakly ionising
fast speed
stopped by 3mm of aluminium
affected by magnetic field
beta +
positron
+1 charge
negligible relative mass
annihilated by electron - virtually zero range
gamma
electromagnetic wave
0 charge
0 mass
very weakly ionising
travels at the speed of light
stopped by several cm of lead/m of concrete
not affected by magnetic field
Ionising properties: Alpha
Alpha particles are strongly positive
Can easily pull electrons off atoms
Ionisation transfers energy from alpha particle to atom
The alpha particle ionises 10,000 atoms per mm in air and loses all its energy
Allow current to flow but don't travel very far - used in smoke alarms
Alpha cannot penetrate the skin but are dangerous is if ingested
They ionise body tissue causing damage
Ionising properties: Beta
Beta-minus particles have lower mass and charge than alpha but higher speed
Knock electrons off atoms
Each beta particle ionises 100 atoms per mm in air and loses its energy
Fewer interactions mean it causes less damage to body tissue
Beta radiation is commonly used to control the thickness of a material
Penetrating power
Record the background radiation count rate when no source is present
Place an unknown source near a Geiger counter and record the count rate
Place a sheet of paper between the source and the Geiger counter and record the count rate
Repeat step 2, replacing the paper with a 3mm thick sheet of aluminium
Control
Control the thickness of sheets of paper, foil, or steel
Material flattened through rollers
The radioactive source is placed on one side and a radioactive detector on the other
The thicker the material, the more radiation it absorbs and prevents from reaching the detector
If too much radiation is being absorbed, the rollers move closer together to make the material thinner
If too little radiation is being absorbed, they move further apart
The inverse-square law
Gamma source emits gamma radiation in all directions
Radiation spreads out further away from the source
Radiation per unit area (intensity) decreases further from the source
$I=$ $\frac{k}{x^2}$
Safety precautions
Radiation is more dangerous the closer it is so hold the source away from your body
Long handling tongs minimise radiation absorbed
Maintain as far away as possible
Background radiation = radiation occurring in buildings, rocks, food, nuclear facilities, cosmic rays
Air
Radioactive radon gas is released from rocks
Emits alpha radiation
Concentration in the atmosphere varies from place to place
The ground and buildings
All rock contains radioactive isotopes
Cosmic radiation
Cosmic rays are particles from space that collide with particles in the atmosphere to produce nuclear radiation
Living things
All plants and animals contain carbon - radioactive carbon-14
Also contains other radioactive materials such as potassium-40
Man-made radiation
Radiation from medical or industrial sources
Measuring radiation
Remove radioactive material and measure background activity for 10 minutes
Bring radioactive material and repeat (count = material + background radiation)
Corrected count = total count - background
Repeat background radiation test
Radiation in medicine
Positives:
Gamma radiation is used as it is weakly ionising and less damaging to body tissue
Radioactive tracers used to diagnose patients without surgery
A short half-life prevents prolonged radiation exposure
The detector is used to detect emitted gamma rays
Gamma rays are used in the treatment of cancerous tumours
Radiation damages all cells so a rotating beam of gamma rays used
Gives a high dose of radiation to tumour and lessens damage to surrounding tissue
Radiation in medicine
Negatives:
Damage to healthy cells isn't prevented and can cause side effects such
Tiredness and reddening or soreness of the skin
Exposure can cause long-term side effects like infertility
Exposure time to radioactive sources is kept to a minimum for medical staff
Radioactive decay = random disintegration of an unstable nucleus by the emission of particles or electromagnetic radiation
The resultant nucleus is more stable
Radioactive emissions = ionising radiation as ions can be created
Individual radioactive decay is random
$\frac{\Delta N}{\Delta t}=$ $-\lambda N\ \ \ \ \ N=$ $N_0e^{-\lambda t}$
Number of atoms = number of moles x Avogadro’s constant
$N=$ $nN_A\ \ \ \ \ N_A=$ $6.02\times10^{23}$
Same equation for activity and number of radioactive material
$A=$ $A_0e^{-\lambda t}\ \ \ \ \ C=$ $C_0e^{-\lambda t}$
Activity = number of unstable radioactive nuclei that decay per second
$A=$ $\lambda N\ \ \ \ \ \lambda$ =the decay constant
Half-life = the average time it takes for the number of unstable nuclei to halve
$P=$ $AE$
$T_{\frac{1}{2}}=$ $\frac{\ln2}{\lambda}=$ $\frac{0.693}{\lambda}$
Calculating half-life
Activity-time graph:
Read off count rate at t=0
Go to half this value
Draw a horizontal line to the curve and a vertical line to the X-axis
Read off half-life where it crosses the x-axis
Repeat for a quarter-and-half answer to check the value for the half-life
Natural log of activity-time graph:
Natural log of number of radioactive atoms/activity against time gives a straight-line graph
The gradient is the negative decay constant
Used to calculate half-life
Carbon dating
78% of earth’s atmosphere is nitrogen
The most common isotope is nitrogen-14
Cosmic rays (protons) decay into neutrons
Rarely replace protons in nitrogen forming carbon-14 and a hydrogen ion
Living things absorb carbon dioxide during photosynthesis and respiration
Only when living
...carbon dating
When they die, the carbon-14 decays back into nitrogen-14 through beta-minus decay
The activity of carbon-14 falls with a half-life of 5730 years
Scientists compare the number of C-14 in material with the expected number of living material and determine the number of half-lives it has gone through
Can calculate the approximate age
Argon dating
93.3% of potassium is potassium-39
6.7% K-41
0.0117% K-40
K-40 used to date volcanic rock
Half-life of 1.25billion years so can date material from longer ago than C-14
11% of decay isn't bonded to anything so is released into the atmosphere
89% of decay turns into argon-40
When volcanoes erupt it contains K-40 and Ar-40
Ar-40 bubbles out
When the lava solidifies calcium-40 and argon-40 build-up
Scientists look at the ratio of Ar-40 left to what was there before
Date rocks above and below an object to determine the period the object must be from
Storing radioactive substances
Some isotopes found in waste products of nuclear power generation have long half-lives
Stored in water tanks
Sealed underground
Prevents damage to the environment and people
Sterilising Medical Equipment
Gamma radiation is used to sterilise medical equipment
It is the most penetrating
It is penetrating enough to irradiate all sides of the instruments
Instruments can be sterilised without removing packaging
In order for a substance to become radioactive, the nuclei have to be affected
Ionising radiation only affects the outer electrons and not the nucleus
The radioactive material is kept securely sealed away from the packaged equipment so there is no chance of contamination
N = number of neutrons
P = number of protons
Most common elements have values of less than 20
Lighter elements are more stable
Nuclear radiation
If a nucleus is unstable it will break down to become more stable
Instability caused by an incorrect number of neutrons or too much energy in the nucleus
Unstable nucleus
Too many nucleons
Too much energy
Light isotopes
Z<20
Stable
Straight line
N=Z
Heavy isotopes
Z>20
Neutron-proton ratio increases
Stable nuclei must have more neutrons than protons
Imbalance in ratio
1-3fm nucleons are bound by strong nuclear force
<1fm strong nuclear force is repulsive
Prevents nucleus from collapsing
>3fm electromagnetic force acts between protons
More unstable
As protons are added, neutrons are needed to be added
Increases distance between protons reducing electrostatic repulsion
Increase binding force, binding nucleons together
Alpha emission
Beneath the line of stability, Z>82
Too many nucleons
More protons than neutrons, but too large to be stable
Strong nuclear force cannot overcome electrostatic repulsion
Beta-minus emission
To the left of the stability line
Isotopes are neutron-rich compared to stable isotopes
Neutron is converted to a proton
Emits beta- particle and electron neutrino
Beta-plus emission
To the right of the stability line
Isotopes are proton-rich compared to stable isotopes
Proton converted to neutron
Emits beta+ particle and electron neutrino
Electron capture
To the right of stability line
Isotopes are proton-rich
When nucleus captures own orbiting electrons
Proton converted to neutron
Releases gamma ray and electron neutrino
Radioactive decay equations
Beta-minus emission = too many neutrons
$X\ _Z^A\ \rightarrow\ \beta\ _{-1}^0+$ $Y\ _{Z+1}^A+$ $\frac{ }{v_e}$
Beta-plus decay or electron capture = too many protons
$X\ _Z^A\ \rightarrow\ \beta\ _{+1}^0+$ $Y\ _{Z-1}^A+$ $v_e$
$X\ _Z^A\ +$ $e\ _{+1}^0\rightarrow Y\ _{Z-1}^A+$ $v_e$
Alpha emission = too many nucleons
$X\ _Z^A\ \rightarrow\ \alpha\ _2^4+$ $Y\ _{Z-2}^{A-4}$
Gamma emission = too much energy
After alpha or beta decay
Loss of excess energy in the nucleus through gamma ray
No change in constituents
Nuclear reactions
In every nuclear reaction energy, momentum, charge, and nucleon number must be conserved
Medical diagnosis
Technetium-99m emits gamma radiation and has a half-life of 6 hours
Long enough to record data but short enough to limit radiation
Decays into a much more stable isotope
Closest approach
Alpha particle stops momentarily and rebounds at 180° due to electrostatic repulsion
When stopped all KE is converted to PE
The alpha particles and gold don't touch
Particle stops at the point where initial KE = PE
$E_K=$ $E_{elec}\ =$ $\frac{Q_{gold}\ \ Q_{alpha}}{4\pi\epsilon_0d}$
To calculate the nucleus charge, the atomic number (Z) is needed
Proton has a charge of +e
Therefore, the charge of the nucleus = +Ze
The distance of closest approach is an overestimate of the nuclear radius
Electron diffraction
Electrons don't interact with the strong nuclear force as they are leptons
Electrons show wave-particle duality so an electron beam can be diffracted
The de Broglie wavelength must be tiny, so the electrons will have high energy
$\lambda=$ $\frac{hc}{E}$
A beam of high-energy electrons will produce a diffraction pattern
The first minimum:
$\sin\left(\theta\right)=$ $\frac{1.22\lambda}{2R}=$ $\frac{0.61\lambda}{R}$
Atomic radius = $5\times10^{-11}m$
Nuclear radius = $1\times10^{-15}m$ = 1 femtometre
Nuclear radius
Linear relationship between nuclear radius and the cube root of the nucleon number
A = nucleon number
R ∝ $A^{\frac{1}{3}}$
$R=$ $R_0A^{\frac{1}{3}}$
$R_0$ is approximately 1.4fm
Nuclear density
The volume each nucleon takes up in a nucleus is almost equal
Nucleons have similar mass (u = mass of 1 nucleon) so all nuclei have similar density
$\rho=$ $\frac{m}{V}=$ $\frac{Au}{\frac{4}{3}\pi R^3}=$ $\frac{Au}{\frac{4}{3}\pi\left(R_0A^{\frac{1}{3}}\right)^3}=$ $\frac{3u}{4\pi R_0^{\ \ 3}}$ =constant
Substitute the values of these constants, nuclear density = $1.45\times10^{17}kgm^{-3}$
Nuclear density is greater than atomic density so the mass must be concentrated in the nucleus
Intensity
Diffraction pattern similar to the light source through a circular aperture
Central bright maxima containing the majority of incident electrons
Surrounded by dimmer maxima
Intensity decreases as the angle of diffraction increases
Mass defect
Mass gained or lost when nucleons are separated or combined
Difference between mass of separated nucleons and mass of nucleus
Energy required to separate
Energy released in combining
$\Delta m=$ $Zm_p+$ $\left(A+Z\right)m_n-m_{total}$
Z = proton number
A = nucleon number
$m_p$ = mass of proton (kg)
$m_n$ = mass of neutron (kg)
$m_{total}$ = measured mass of nucleus (kg)
Electrostatic repulsion between protons
Requires binding energy to keep nucleons together
Binding energy
Work done to separate all nucleons
Outside range of strong nuclear force
3-5fm
MeV
Stability of nucleus based on binding energy per nucleon
Energy and mass are proportional
total energy of nucleus is less than sum of energies of its constituent nucleons
formation of nucleus from system of isolated protons and neutrons is exothermic reaction
releases energy
E=mc2
Nuclear reactions involve changes in nuclear binding energy
chemical reactions involve changes in electron binding energy
Nuclear reactions produce much more energy than chemical reactions