RADIOACTIVITY

Ionise atoms by removing some of their electrons, leaving positive ions

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• Alpha
  • 1 alpha particle = 1 helium nucleus = 2 protons + 2 neutrons
  • +2e

• Beta-minus
  • Fast-moving electrons
  • -e

• Beta-plus
  • Fast-moving positrons
  • +e

• Gamma
  • High-energy photons
  • 0e
  • λ < 10^-13 m
  • Travel at the speed of light

Uniform electric field provided by two oppositely charged parallel plates

• Alpha particles: deflected towards the negative plate (↑ mass so ↑ deflection)

• Beta-minus particles: deflected towards the positive plate

• Beta-plus particles : deflected towards the negative plate

• Gamma rays: uncharged so not deflected

Alpha

• Large mass and charge so strongly ionising
• Short range in air
• Completey absorbed by paper

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Beta

• Small mass and charge so less ionising
• Longer range in air
• Mostly absorbed by aluminium

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Gamma

• No charge so even less ionising
• Count rate decreases exponentially with thickness of lead absorber
• Mostly absorbed by lead

• Ionising

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• Can cause damage to living cells

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• Store in lead-lined containers

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• Use a pair of tongs with long handles to keep them away from your body

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• Wear gloves

^A_ZX → ^{A - 4}_{Z - 2}Y + ⁴₂He

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• 2 protons + 2 neutrons removed from the parent nucleus

• Atomic number decreases by 2, so the element is different

• Nucleon number decreases by 4

• Total atomic and nucleon numbers conserved

• Energy released

^A_ZX → ^A_{Z + 1}Y + ⁰_-1e + v_e

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• Caused by the weak nuclear force

• Too many neutrons for stability- a neutron decays into a proton

• Atomic number increases by 1, so the element is different

• Nucleon number stays the same

• Total atomic and nucleon numbers conserved

• Energy released

^A_ZX → ^A_{Z - 1}Y + ⁰₁e + v_e

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• Caused by the weak nuclear force

• Too many protons for stability- a proton decays into a neutron

• Atomic number decreases by 1, so the element is different

• Nucleon number stays the same

• Total atomic and nucleon numbers conserved

• Energy released

^A_ZX → ^A_ZX + ɣ

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• When a nucleus has surplus energy following an alpha or beta emission

• Atomic number stays the same, so the element stays the same

• Nucleon number stays the same

• Energy released

• We cannot predict

• when a particular nucleus will decay

• which nucleus will decay next

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• Each nucleus has the same chance of decaying per unit time

The decay of nuclei is not affected by

• the presence of other nuclei

• external factors such as pressure

Average time taken for half the number of active nuclei in a sample of an isotope to decay

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N = N_o x 0.5ⁿ 

• N = final number of nuclei
• N_o = initial number of nuclei
• n = number of half lives

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t_1/2 = 0.5N

∴ N decreases exponentially with t

• Rate of decay of nuclei

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• Number of alpha/ beta/ gamma particles emitted per unit time

ΔN ∝ NΔt

• ΔN = number of nuclei decaying
• N = number of undecayed nuclei
• Δt = time

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ΔN / Δt ∝ - N

• - shows that N decreases as t increases

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ΔN / Δt = rate of decay of nuclei = activity

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A = λN

• A = activity
• λ = decay constant (probability of decay of an individual nucleus per unit time)

A = ΔN / Δt and A = - λN

ΔN / Δt = - λN

N = N_oe^-λt

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A = A_oe^-λt

C = C_oe^-λt

N = N_o / 2 when t = t_1/2

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N_o / 2 = N_oe^-λt_1/2

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1/2 = e^-λt_1/2

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2 = e^λt_1/2

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In(2) = In(e^λt_1/2)

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In(2) = λt_1/2 as In(e^kx) = kx

C-12 = stable isotope

C-14 = unstable radioactive isotope (t_1/2 = 5730 years)

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C-14 formed in upper atmosphere

¹⁴₇N + ¹₀n → ¹⁴₆C + ¹₁p

n formed from collisions between high-speed protons in cosmic rays from space and atoms in upper atmosphere

t_1/2: ¹⁴₆C → ¹⁴₇N + ⁰_-1e + v_e

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C-14 required by plants for photosythesis

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂

C-12 : C-14 = 1.3 x 10¹²

Constant

The same in all living things and the upper atmosphere

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When things die, they stop taking in carbon

Amount of C-12 stays the same

Amount of C-14 decreases over time

Ratio decreses over time

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Time since the organism died determined by comparing the C-12 : C-14 ratios of the dead and similar living material

• Assumes the ratio of C-12 : C-14 has remained constant over time

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• Increased emission of CO₂ due to burning fossil fuels may have reduced the ratio

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• Natural events such as volcanic eruptions may have reduced the ratio

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• The small amounts of C-14 in organisms means that the activities are extremely small