Bananas are a natural source of radioactive Number of Equivalent exposure . 100,000,000 Fatal dose (death within 2 weeks) Typical targeted dose used in radiotherapy 20,000,000 Eating one banana = 1 (one session) BED = 0.1 μSv = 0.01 mrem 70,000 Chest CT scan 20,000 Mammogram (single exposure)

200 - 1000 Chest X-ray

Living in a stone, brick or concrete 700 building for one year

400 Flight from London to New York

100 Average daily background dose

50 Dental X-ray

Yearly dose from living near a nuclear power 1 - 100 station

1 P2 Nuclear and Parcle Physics - Dan Protopopescu Neutron

• Neutrons are components of atomic nucleus, zero electric charge, mn ≈ mp Neutron-induced fission n • Sources of neutron radiaon: n n – interacon of cosmic radiaon with the atmosphere n – neutron emission during fission (e.g. in nuclear reactors) Neutron spallaon – parcle accelerators (spallaon sources, e.g. ISIS, SNS) • Interacon with maer: – neutron capture (n is captured by a nucleus and α or γ is emied) – elasc scaering (recoiling nuclei collide and produce charge or Hydrogen-rich materials make the best scinllaon light that can be neutron shielding: e.g. water, detected) polyethylene, paraffin wax, concrete

P2 Nuclear and Parcle Physics 2 Neutron RBE

RBE figures set by the Internaonal Commission on Radiological Protecon (ICRP):

(2003)

P2 Nuclear and Parcle Physics 3 Radiation definitions and facts

• Definitions: – Radiaon - energy traveling in the form of particles or waves, for example: microwaves, radio waves, light, medical X-rays, alpha, beta, gamma radiation – Radioacvity - a natural process through which unstable of an element radiate excess energy in the form of particles or waves – Radioacve material - material that emits radiation – Radioacve contaminaon - radioactive material in unwanted places • Important facts: – Radiation is commonplace – A person exposed to radiation does not become contaminated, except for neutron radiation which can induce radioactivity – Contamination is the result of direct contact with removable radioactive material – The distinction between harmful and safe depends on quantity. This is true about everything from paracetamol to arsenic – Dose is important

4 P2 Nuclear and Parcle Physics - Dan Protopopescu Nuclear and Particle Physics Part 2: Nuclei

Dr. Dan Protopopescu Kelvin Building, room 524 [email protected]

5 The discovery of the nucleus: Rutherford Scattering

• The Thomson model of the (the plum pudding model) assumed that electrons were embedded in a posive charge with an atomic size ~10-10m • Firing α-parcles at Au foil Geiger and Marsden (1909) were expecng to see the alphas passing through and undergoing only a small amount of scaering. • However, they observed an amazing result: some of the alphas were scaered by very large angles up to almost 180o

P2 Nuclear and Parcle Physics 6 Rutherford Scattering

• Rutherford interpreted these results as the scaering of the alpha parcle from a very small dense core of posive charge in the centre of the atom: the nucleus

Ernest Rutherford: “it was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a 15- inch shell at a piece of ssue paper and it had come back and hit you”

• This was the basis for the Bohr model of the atom • Chadwick later discovered the neutron

P2 Nuclear and Parcle Physics 7 Atoms and nuclei

• Atoms are electrically neutral – Z electrons orbit a nucleus containing Z protons – Z is called the atomic number - and is the key to chemistry – Atomic size ~10-10m • Nuclei form the dense core of the atom – the nucleus – Consist of protons and neutrons – Size of the nucleus ~10-15 m

P2 Nuclear and Parcle Physics 8 Measuring nuclear radii

• To ‘see’ a nucleus requires very small wavelengths -> one can use electrons • Scaering electrons off a nucleus produces a diffracon paern • Note that this measures the charge radius since the electron scaering off the nucleus is governed by electromagnec interacon

P2 Nuclear and Parcle Physics 9 Numerical example

De Broglie wavelength is given by

λ = h/p

For an electron of 400 MeV energy, p = 400 MeV/c

λ = (4.13×10-21 MeV⋅s × 3×108)/400 MeV/c ≈ 3fm where 1fm = 10-15 m

This is comparable with the size of the nucleus.

P2 Nuclear and Parcle Physics 10 Nuclear charge radius

ORY

R~A1/3

1 3 The central density is the same for all nuclei R = R0 A where R0 = 1.2 fm

P2 Nuclear and Parcle Physics 11 Nuclear nomenclature

Lead-208:

• X = chemical symbol • Z = number of protons 82 protons • N = number of neutrons 126 neutrons (= 208 - 82) – (this oen not quoted as it is redundant) Carbon-12: • A = mass number A = Z + N

P2 Nuclear and Parcle Physics 12 Some more nomenclature

• Isotopes: – Nuclei with the same number of protons Z (same chemical element) but different numbers of neutrons • Isotones: – Nuclei with the same number of neutrons but different proton number • Isobars: – Nuclei with the same mass number but different numbers of protons and neutrons

P2 Nuclear and Parcle Physics 13 Nuclear masses

• Nuclear masses – Are measured using mass spectrometers – Masses are measured in atomic mass units: u – 12C is defined to be exactly 12.0u Charge Mass (u) Mass (MeV/c2) 1u = 931.50 MeV/c2 Proton +1e 1.00727647 938.280 Neutron 0 1.00866501 939.573 Electron -1e 5.48580x10-3 0.511003

P2 Nuclear and Parcle Physics 14 Nuclear mass and binding energy

The mass of a nucleus can be written as: Z 2 2 2 mNc = mAc − Zmec + ∑Be i=1 Atomic mass Electron mass Electron binding energy energy energy

€ Electron binding energy can be ignored compared to the atomic mass energy

Electronic binding energy/atomic mass energy ~10-100keV/A x 1000MeV

15 P2 Nuclear and Parcle Physics - Dan Protopopescu How stable is a nucleus ? Binding energy

- The binding energy, B, of a nucleus is the difference in mass energy between the free parcles and the bound state - This is related to the stability of nuclei, the greater the binding energy the more stable the nucleus

- It is oen useful to look at binding energy/nucleon: B/A i.e. the energy required to remove a nucleon from the nucleus, similar to atomic ionisaon energy ⎧ B = ⎨ Zm + Nm − m A X − Zm c 2 ⎩ p n [ ( ) e ]} Free nucleons Bound state

B Zm 1H Nm m A X c 2 = [ (1 ) + n − ( )]

16 P2 Nuclear and Parcle Physics - Dan Protopopescu

€ Binding energy per nucleon

Fe is the most stable nucleus

Light nuclei are Fusion Fission not stable but 4 2He – alpha parcles are

17 P2 Nuclear and Parcle Physics - Dan Protopopescu What nuclei exist?

Z=N

There are 214 stable nuclides, up to Z=82 (Pb)

There are 3896 nuclides known today

18 P2 Nuclear and Parcle Physics - Dan Protopopescu The search for new elements

2009 Poster

19 P2 Nuclear and Parcle Physics - Dan Protopopescu Nuclear decay and radioactivity

Change in nuclear state ⇔ Radiaon

Nuclei decay via: • α-decay • β-decay • γ-decay – nuclei have energy levels like atoms, γ-rays are emied when an nucleus de-excites – does not change Z or N • Nucleon emission – Emission of n or p, via a process similar to α-decay • Spontaneous fission

P2 Nuclear and Parcle Physics 20 Alpha decay

A A-4 4 ZXN Z-2YN-2+ 2He2

240 236 4 94Pu146 92U144+ 2He2

Quantum tunnelling

P2 Nuclear and Parcle Physics 21 Beta decays

β-decay: np+e-+ν A A - ZXN Z+1YN-1+ e + νe 14 14 + 6C8 7N7+e +νe

β+-decay: pn+e++ν

A A + 10 10 + ZXN Z-1YN+1+ e + νe 6C4 5B5+e +νe

Electron capture: e-+pn+ν e-+A X A Y + ν Z N Z-1 N+1 e - 11 11 e + 6C5 5B6+νe

P2 Nuclear and Parcle Physics 22 The 238U Decay Chain

Z =

Only main decays are shown (γ-emiers are not indicated)

P2 Nuclear and Parcle Physics 23 What nuclei exist

β-stability valley:

N

24 P2 Nuclear and Parcle Physics - Dan Protopopescu Stability

P2 Nuclear and Parcle Physics 25 Beta-stability valley

Using the semi-empirical equaon for the binding energy: Z 2 (A − 2Z)2 B (Z,A) = a A − a A2 / 3 − a − a tot v s c A1/ 3 a A

M(Z,A) = Z⋅ M p + (A − Z)Mn − Btot (Z,A) (A − 2Z)2 A2 − 4AZ + 4Z 2 $ 4Z 2 ' aa = aa = aa& A − 4Z + ) A A % A ( * a - $ a 4a ' M = A M − a + s + a + Z M − M − 4Za + Z 2& c + a ) +, n v A1/ 3 a ./ [ p n a ] % A1/ 3 A ( This the equaon of a parabola M(Z) = a + bZ + cZ2 Minimising M: € # ∂M & % ( = 0 = b + 2cZA $ ∂Z ' A Z 1 81 A ≈ A 2 80 + 0.6A2 / 3

P2 Nuclear and Parcle Physics 26

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