Module 6: C25 - Radioactivity Flashcards
What makes up Alpha radiation
Alpha radiation consists of positively charged particles. Each alpha particle comprises two protons and two neutrons (a helium nucleus), and has charge +2e where e is the elementary charge.
What makes up Beta radiation
Beta radiation consists of fast-moving electrons (β^-) or fast moving positrons (β^+). A beta-minus particle has charge -e and a beta-plus particle has charge +e
What makes up Gamma radiation
Gamma radiation consists of high-energy photons with wavelengths less than about 10^-13m. They travel at the speed of light and carry no charge.
How does a uniform Electric Field affect the different types of radiation
A uniform electric field provided by two oppositely charged parallel plates can help us distinguish between the types of radiation.
The beta-minus particles (electrons) are deflected towards the positive plate, whilst the positive alpha and beta-plus (positron) particles are deflected towards the negative plate. Alpha particles are deflected less than beta particles, because of their greater mass. The paths of the beta-minus and beta-plus particles are mirror images. Gamma rays are not deflected, because they are unchanged (and do not have an electric charge of their own).
How does a uniform Magnetic Field affect the different types of radiation
For a uniform magnetic field, the direction of the force on each particle can be determined using Fleming’s left hand rule. Again, the uncharged gamma rays are not deflected. The heavier alpha particles are deflected less than the lighter beta particles.
How far can Alpha radiation travel
The large mass and charge of alpha particles mean they interact with surrounding particles to produce string ionisation, and therefore they have a very short range in air. It takes only a few centimetres of air to absorb most alpha particles. A thin sheet of paper completely absorbs them.
How far can Beta radiation travel
The small mass and charge of beta particles make them less ionising than alpha particles. This means that they have a much longer range in air, about a metre. It takes about 1-3mm of aluminium to stop most beta particles.
How far can Gamma radiation travel
Gamma rays have no charge, and this makes them even less ionising the beta particles. You can show that for gamma rays the count rate decays exponentially with the thickness of lead absorber. You need a few centimetres of lead to absorb a significant proportion of gamma rays.
What forms of protection can be used when using radioactive sources
When transferring radioactive sources, for your own protection, you must use a pair of tongs with long handles in order to keep the source as far from your body as possible. You should never handle radioactive sources with bare hands.
Alpha Radiation:
- Symbol
- Electric Charge
- Stopped By
- Ionising ‘Power’
- What Nature Is It?
Symbol:
α
Electric Charge:
+2e
Stopped By:
Sheet of paper
Ionising Power:
Very strong
What Nature Is It:
Helium Nucleus
Is there a trend between how ionising radiation is and how quickly it loses energy
The most ionising one has the largest electric charge and is the least penetrating. The most ionising lose energy the quickest
What is Radioactive Decay?
Radioactive decay is the emission of a radioactive particle from an unstable nucleus
What Happens in Transmutation?
Radioisotopes would like to be stable isotopes so they are constantly changing to try and stabilize. In the process, they will release energy and matter from their nucleus and often transform into a new element. This process, called transmutation. The radioactive decay and transmutation process will continue until a new element is formed that has a stable nucleus and is not radioactive.
Note: The nucleus before the decay is known as the parent nucleus, and the new nucleus after the decay is. called the daughter nucleus.
Alpha Radiation:
- Symbol
- Mass
- Speed
Symbol:
⁴₂He or α
Mass:
4.00151
Speed:
~10^6
Beta-minus Radiation:
- Symbol
- Mass
- Speed
Symbol:
⁰ -₁e or β^- or e^-
Mass:
0.00055
Speed:
~10^8
Beta-plus Radiation:
- Symbol
- Mass
- Speed
Symbol:
⁰+₁e or β^+ or e^+
Mass:
0.00055
Speed:
~10^8
Gamma Radiation:
- Symbol
- Mass
- Speed
Symbol:
γ (also ⁰₀γ)
Mass:
0
Speed:
Speed of Light (3x10^8 ms^-1)
What things are conserved in all Nuclear Reactions?
In all nuclear reactions:
nucleon number A and proton number Z must be conserved
Conservation of mass and energy are interchangeable:
The energy is released in nuclear reactions is produced from mass.
What happens in Alpha Decay (+ nuclear transformation equation)
The nuclear transformation equation below shows a parent nucleus X decaying into a daughter nucleus Y when it emits an alpha particle.
ᴬzX —>ᴬ-⁴z-₄Y + ⁴₂He
(Energy is also released in the decay)
Worked Example:
A radium-226 nucleus ²²⁶₈₈Ra decays by alpha emission to become a nucleus of radon (Rn). Predict the isotope of radon produced in this decay.
Step 1:
Determine the final nucleon and proton numbers for the radon nucleus.
A = 226 - 4 = 222
Z = 88 - 2 = 86
Step 2:
Represent the daughter nucleus using the correct chemical symbol and A and Z numbers.
Daughter Nucleus: ²²²₈₆Rn
Beta-minus nuclear Transformation equation
The nuclear transformation equation for Beta-minus decay is:
ᴬzX —> ᴬz+₁Y + ⁰-₁e + ̅νe
Beta-plus nuclear Transformation equation
The nuclear transformation equation for Beta-plus decay is:
ᴬzX —> ᴬz-₁Y + ⁰+₁e + Ve
What happens in Gamma Decay (+ nuclear transformation equation)
ᴬz X —> ᴬz X + γ
The only stable isotope of aluminium is ²⁷₁₃Al. State and explain whether the isotope ²⁹₁₃Al is proton rich or neutron rich
It is neutron rich, as there are more neutrons than protons (less than half of the nucleus is made up of protons). Therefore it requires β+ decay
Example Question:
A nucleus of uranium-234 (²³⁴₉₂U) transforms into an isotope of lead (Pb) after emitting five alpha particles. Predict the lead isotope formed
2x5 = 10
4x5 = 20
234-20 = 214
92-10 = 82
²¹⁴₈₂Pb
Why do Decay Chains happen?
The radioactive decay is complex, because the daughter nuclei can themselves be radioactive. An ancient rock containing uranium will therefore also contain its daughters, their daughters, and so on. All of them will emit their own characteristic radiation.
Beta Radiation:
- Symbol
- Electric Charge
- Stopped By
- Ionising ‘Power’
- What Nature Is It?
Symbol:
β
Electric Charge:
-1e
Stopped By:
Aluminium Foil
Ionising Power:
Strong
What Nature Is It:
Electron
Gamma Radiation:
- Symbol
- Electric Charge
- Stopped By
- Ionising ‘Power’
- What Nature Is It?
Symbol:
γ
Electric Charge:
0
Stopped By:
Few cm of lead or few metres of concrete
Ionising Power:
Weak
What Nature Is It:
High frequency EM Wave
There is an experiment where a Geiger-Müller (GM tube and a counter are used to investigate the absorption of α, β^-, and γ radiation by different materials.
Why is it not possible to carry out a similar experiment in a school or college laboratory with β^+ particles (positrons)?
Any positrons would be annihilated by surrounding electrons, meaning β+ radiation cannot occur in the lab (it could happen in a vacuum)
What makes radioactive decay random
- We cannot predict when a particular nucleus in a sample will decay or which one will decay next
- Each nucleus within a sample has the same chance of decaying per unit time
What makes radioactive decay spontaneous
Radioactive decay is spontaneous, because the decay of nuclei is not affected by:
- The presence of other nuclei in the sample
- External factors such as pressure
Describe what is meant by the spontaneous and random nature of radioactive decay of unstable nuclei
The fact that decay is spontaneous shows that the decay is not affected by the nucleus’s surroundings or external factors, while it’s random nature means that it could decay at any given time, as we cannot predict which nucleus could decay next.
How can you simulate the random behaviour of unstable nuclei by using popcorn?
The kernels represent the undecayed nuclei and a single pop represents a single decay. At the start, there are many unpopped kernels and the popping rate is high. As the amount of unpopped corn decreases, so does the popping rate.
Half-life definition
The half-life of an isotope is the average time it
takes for half the number of active nuclei in the
sample to decay.
What is ‘Activity A’
The activity A of a source is the rate at which the nuclei is decay or disintegrate.
Or
Number of alpha, beta, or gamma photons
emitted from the source per unit time.
What is activity measured in (and what is it equal to?)
Activity is measured in decay per second.
An activity of one decay per second is equal to 1 becquerel. (Bq)
Worked Example:
The activity of an alpha-emitting source is 5.0x10^12 Bq. The kinetic energy of each alpha particle is 4.0MeV. Calculate the power emitted by this source.
Step 1: Calculate the energy of each alpha particle.
1eV = 1.60x10^-19 J
Therefore,
Energy of an α-particle = 4.0x10^6 x 1.60x10^-19
= 6.4x10^-13 J
Step 2: The activity means that there are 5.0x10^12 α-particles emitted per second.
Therefore, energy emitted per second = 5.0x10^12 x 6.4x10^-13
= 3.2Js^-1
Step 3: Power is the rate of energy emitted.
Therefore, power = 3.2W
What is the Decay constant λ
Decay constant 𝝺, can be defined as the probability of decay of an individual nucleus per unit time.
The decay constant has the SI unit:
s^-1 (or h^-1 or even y^-1, but not Bq)
Equation for Activity A of the source (involving the decay constant)
A = λN
What is the number of nuclei disintegrating directly proportional to?
In a small interval of time Δt, it would be reasonable to assume that the number of nuclei disintegrating would be directly proportional to both N and Δt.
ΔN ∝ NΔt
Therefore,
ΔN/Δt = -N
Why is the minus sign included in the equation
ΔN/Δt ∝ -N
The minus sign is included to show that the number of nuclei is decreasing with time. ΔN/Δt is the rate of decay of the nuclei, that is, the activity A of the source.
Equation to find decay constant (involving activity A and number of nuclei)
A = λN
Equation for exponential decay of Nuclei
N = No e^-λt
The decay constant 𝝺 of an isotope is related to its half-life t1/2. Use the decay equation to determine this link.
t = t1/2
N = No/2
N = No e^-λt
No/2 = No e^-λt1/2
1/2 = e^-λt1/2
ln 1/2 = -λt1/2
λt1/2 = ln 2
t1/2 = ln 2 / λ
The half-life of protactinium is 73 seconds. A freshly-prepared sample has an activity of 30 kBq.
(i) Calculate the decay constant of protactinium.
(ii) How many atoms of protactinium are initially present in the sample?
(iii) What would be the activity of the sample 2.0 minutes after preparation?
i)
t1/2 = 73s
λt1/2 = ln 2
73λ = ln 2
λ = 9.50x10^-3
ii)
A = λΝ
30,000 = 9.495x10^-3 No
No = 315902 initial nuclei
iii)
A = Ao e^-λt
A = 30,000 e^-9.5x10^-3 x 120
A = 9594.6 Bq
A = 9600 Bq
This question is about a space probe which is in orbit around the Sun.
The power source for the instrumentation on board the space probe is plutonium-238, which provides 470W initially.
Plutonium-238 decays by α-particle emission with a half-life of 88 years.
The kinetic energy of each α-particle is 8.8x10^-13J
i) Calculate the number N of plutonium-238 nuclei needed to provide the power of 470W
ii) Calculate the power P still avaliable from the plutonium p-238 source 100 years later
i)
Po = 470W
t1/2 = 88 years = 2775168000s
KE = 8.8x10^-13 J per α-particle
λt1/2 = ln 2
λ = 2.50x10^-10
P = E/T
P/E = 1/T
A = P/E
A = 470 / 8.8x10^-13
A = 5.34x10^14 Bq
A = λN
N = 5.34x10^14 / 2.5x10^-10
N = 2.1x10^24
ii)
P = Po e^-λt
P = 470 e ^-2.50x10^-10 x 315360000
P = 213.65 W
P = 214 W
What is Carbon Dating
Carbon dating is a method for determining the age of
organic material, by comparing the activities, or the ratios, of carbon-14 to carbon-12 nuclei of the dead material of interest and similar living material.
In carbon dating, it has been assumed that the ratio of carbon-14 atoms to carbon-12 atoms has remained constant over time in living organisms (1.3x10^-12).
Explain what factors do you think can cause changes in this ratio?
- Increased emission of carbon dioxide due to burning fossil fuels may have reduced this to zero.
- Natural events such as: volcanic eruptions and solar flares from the sun
- Testing of nuclear bombs
How is carbon-14 created in the atmosphere
High-speed protons in cosmic rays from space colliding with atoms in the upper atmosphere produce neutrons. These neutrons in turn collide with nitrogen-14 nuclei in the atmosphere,sphere to form carbon-14 nuclei. The carbon-14 nuclei eventually emit beta-minus particles (electrons) and become nitrogen-14 again, so the amount of nitrogen-14 in the atmosphere is replenished
Why can’t you use carbon-14 to date rocks or meteors
You cannot used carbon-14 to date rocks on the Earth or meteors formed during the creation of the Solar System, because it’s half life is not long enough for these ages
What elements do geologists used to date rocks and meteors instead of carbon-14
Instead, geologists use the decay of rubidium-87 to date ancient rocks. Nuclei of rubidium-87 emit beta-minus particles and transform into stable nuclei of strontium-87. The half-life of the isotope rubidium-87 is about 49 billion years, so it is a good candidate for dating ancient rocks
