Nuclear Radius Flashcards
Describe how the distance of closest approach is used to estimate the radius of an atom
- An alpha particle fired at a gold nucleus will have an initial kinetic energy which can be measured
- As it moves towards the positively charged nucleus it will experience an electrostatic force of repulsion and slow down as its kinetic energy is converted to electric potential energy
- The point at which the particle stops and has no kinetic energy is its distance of closest approach
- Its electrical potential energy is equal to its initial kinetic energy due to conservation of energy
- Therefore the alpha particle’s kinetic energy can be equated to electrical potential energy in order to find the radius
Describe the Distance of Closest Approach Equation
Ek = Q /4π x ε0 x r
Kinetic Energy of Alpha Particle = Charge / 4π x Permetivity of Free Space x Distance
Why is Electron Diffraction more accurate the Distance of Closest Approach
- Electrons are leptons meaning they will not interact with nucleons in the nucleus through the strong nuclear force as an alpha particle would
- Alpha Particles will give an overestimate for the radius
- Electron diffraction gives a far more accurate estimate of nuclear radius
Describe how Electron Diffraction gives an estimate for the radius of an atom
- The electrons are accelerated to very high speeds so that their De Broglie wavelength is around 10-15 m
- They are directed a very thin film of material in front of a screen causing them to diffract through the gaps between nuclei and form a diffraction pattern
- The diffraction pattern formed with a central bright spot, which get dimmer as you move away from the centre, using this pattern you can plot a graph of intensity against diffraction angle from which you can find the diffraction angle of the first minimum
- Using this measurement you can find an estimate of nuclear radius by using the following formula: sin θ = 0.61λ/ R
What is the Approximate Radius of a Nucleus
1 x 10-15 m
Describe the Graph of Intensity against angle for electron diffraction by a nucleus
sin θ = 0.61λ / R
Describe the Graph of Nuclear Radius against Nucleon Number
Describe the Graph of the Natural Log of the Nuclear Radius against the Nucleon Number
R = kAn
ln R = ln (k) + n ln (A)
The gradient = 1/3
Y-intercept = ln (k)
What is the Nuclear Radius Equation
R = R0 x A1/3
Radius of the Nucleus = The constant R0 x Nucleon Number 1/3
What is the value of R0
1.4 fm
(It will normally be given in the question)
Describe how the Nuclear Radius Equation shows that Nuclear Density is Constant
Density = Mass / Volume
Density = A x mass nucleon / 4/3 π R3
Density = A x massnucleon / 4/3 π x (R0 x A1/3) 3
Density = A x massnucleon / 4/3 π x R03 x A
Density = massnucleon / 4/3 x R03
Density is a Constant Value
What is the Nuclear Density of a Nucleus
Density = massnucleon / 4/3 x x π R03
Density = 1.45 x 1017 kg m-3
What does the value of the Nuclear Density tell you about any nucleus
The nuclear density is much larger than the density of an atom, suggesting an atom is mostly empty space with most of its mass concentrated in its centre
What is meant by the random nature of radioactive decay
- There is equal probability of any nucleus decaying
- It cannot be known which particular nucleus will decay next
What is radioactive half life
Half-life is time for the number of nuclei to halve for a particular isotope
What is the Radioactive Decay Constant
The probability of a nucleus decaying per unit time
What are the equations for radioactive decay
Δ N / Δ t = - λ N
Change in the number of Nucli / Change in Time = - Constant Decay Probability x Number of Nucli
N = N0 x e
Write the radioactive decay equation in the form y = mx + c
- N = N0 x e-λt
- ln (N) = ln(N0 e -λt )
- ln(N) = ln(N0) +ln(e -λt )
- ln (N) = ln(N0) - λt
- ln(N) = - λt+ ln(N0)
- y = mx + c
What is the Activity of a radioactive sample
The number of nuclei that decay per second
What is Activity measursed in
Bq (decays per second)
What are the Equations for Activity
A = Nλ
Activity = Number of Nucli x Decay Constant Probability
A = A0 x e-λt
Acivity = Initial Activity x e - Decay Constant Probability x Time
What is the Equation for Half Life
T 1/2 = ln 2 / λ
Half Life = ln 2 / Decay Constant Probability
What are the Applications of knowing a Nucleus’ Half Life
- Dating of objects - nuclei with a long half-life such as carbon-14, which has a half-life of 5730 years can be used to date organic objects, such as those found in archaeological sites. This is done by measuring the current amount of carbon-14 and comparing it to the initial amount
- Medical diagnosis - nuclei with relatively short half-lives are used as radioactive tracers in medical diagnosis
- How to store nuclei - nuclei with an extremely long half-life will have to be suitably stored, for example in steel casks underground, to prevent these nuclei from damaging the environment and the people
Describe the Graph of Number of Neutrons against Number of Protons for a Stable Nucli and Non-Stable Nucli
What are the 4 reasons why a nucleus may become unstable
- It has too many neutrons - decays through beta-minus emission or sometimes by neutron emission
- t has too many protons - decays through beta-plus emission or electron capture
- It has too many nucleons - decays through alpha emission
- It has too much energy - decays through gamma emission (this usually occurs after a different type of decay, such as alpha or beta decay because the nucleus becomes excited and has excess energy)
Describe the energy level diagram for a nucleus undergoing alpha decay
Describe the energy level diagram for a nucleus undergoing beta minus decay
Explain why Technetium-99m is used in medical diagnosis
- Technetium-99m is a pure gamma emmited
- Gamma Radiation is weakly ionising and is easily detectable
- It only has a half life of 6 hours making it short enough to have limited exposure but long enough for tests to be carried out
