Nuclear Notes

Nuclear Notes - Notes on Nuclear Physics Dr. Robert Geller...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Notes on Nuclear Physics Dr. Robert Geller Physics Department University of California, Santa Barbara rhmg@physics.ucsb.edu Nuclear Physics (electric) (nuclear) The nuclear force (always a4rac5ve) keeps protons from flying apart. Also called the STRONG FORCE. NUCLEAR DENSITY: A nucleus has the same density as stuffing 20 MILLION elephants into a teaspoon!! Atomic density (not nuclear density) is what we experience all around us. Most of an atom, whose size comes from the electron orbitals, is just empty space. Nuclear Stability and Radioac5vity Unstable atoms CHANGE, giving up some energy and ejec5ng either par5cles or light (gamma rays). This DECAY can occur in frac5ons of a second, or take billions of years. Unstable par5cles are called RADIOACTIVE Example… Techne5um:  ­ 43 protons  ­  no stable forms  ­  mostly man made  ­  used for radiology This view of atoms doesn’t indicate stability, nor the many isotopes…. Stable Atoms 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) Stable atoms plo4ed in black “Z” is the number of protons, or “ATOMIC NUMBER” Stable Atoms 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) Stable atoms plo4ed in black (they tend to need extra neutrons to “glue” nucleus together against proton repulsion (N>Z)) Stable Atoms 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) Too many neutrons – Pauli Exclusion principle breaks atom Causes of instability Too many protons – repulsion breaks atom Stable Atoms 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) 2. Ager LEAD with 82 protons, there are no stable atoms. unstable Stable Atoms 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) 2. Ager LEAD with 82 protons, there are no stable atoms. 3. MANY other isotopes can be found or created outside the “valley of stability”. These are in the colored shaded regions. They are UNSTABLE, and emit energy when they DECAY. Emi$ed par+cles: Electrons, B ­ Positrons, B+ Alpha par5cles Stable Atoms  ­ summary 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) 2. Ager LEAD with 82 protons, there are no stable atoms. 3. MANY other isotopes can be found or created outside the “valley of stability”. These are in the shaded region. They are UNSTABLE, and emit energy when they DECAY. 4. As labeled, different unstable atoms can decay in different ways. G 12. Which of the following is true? A. Elements can only have one stable isotope B. Elements can only have one radioac5ve isotope. C. Isotopes of the same element have the same number of protons. D. Isotopes of the same element have the same number of neutrons. E. Stable elements have equal numbers of protons and electrons. Raphex Stable Atoms  ­ summary 1.  For a given number of protons, there are only a few stable isotopes (i.e. differing number of neutrons) 2. Ager LEAD with 82 protons, there are no stable atoms. 3. MANY other isotopes can be found or created outside the “valley of stability”. These are in the shaded region. They are UNSTABLE, and emit energy when they DECAY. 4. As labeled, different unstable atoms can decay in different ways. (where are gamma ray emi4ers??) γ Nuclear Radia5on – Types of Emission GAMMA RAYS: These are very high energy photons. Just as electron transi5ons can release X ­rays, a nucleus in an “excited” state can “drop down” by emiong a photon. The energy is HIGH, around 1000 KeV, or 1 MeV, and these are called GAMMA RAYS analogy γ Nuclear Radia5on – Types of Emission GAMMA RAYS: These are very high energy photons. Just as electron transi5ons can release X ­rays, a nucleus in an “excited” state can “drop down” by emiong a photon. The energy is HIGH, around 1000 KeV, or 1 MeV, and these are called GAMMA RAYS This is an ISOMERIC TRANSITION which means there’s no change in the number or neutrons or protons. analogy γ Nuclear Radia5on – Types of Emission GAMMA RAYS: These are very high energy photons. Just as electron transi5ons can release X ­rays, a nucleus in an “excited” state can “drop down” by emiong a photon. The energy is HIGH, around 1000 KeV, or 1 MeV, and these are called GAMMA RAYS This is an ISOMERIC TRANSITION which means there’s no change in the number or neutrons or protons. Nuclear Radia5on – Types of Emission γ − β or e β +or e GAMMA RAYS: These are very high energy photons. − BETA: ELECTRONS, POSITRONS An5ma4er electrons (called + positrons) can also shoot out. These are also called BETA PARTICLES. A NEUTRON can decay and become a PROTON, but it emits an ELECTRON. A proton can also change to a neutron, and then it emits a positron. (just balance the electric charge to figure these out!) When a neutron decays somewhere in a nucleus: 1. One neutron disappears 2. A NEW PROTON appears in nucleus, which CHANGES THE TYPE OF ATOM (causing a change of Z +1) 3. An electron, or Beta minus, is EMITTED − β or e − decay We wont look at these + β or e + decay € For this decay, a proton turns into a neutron. The atomic number DECREASES by Z  ­1 Nuclear Radia5on – Types of Emission γ GAMMA RAYS: These are very high energy photons. β −or e − β +or BETA: ELECTRONS, POSITRONS An5ma4er electrons (called e + positrons) can also shoot out. These are also called BETA PARTICLES. Nuclear Radia5on – Types of Emission γ GAMMA RAYS: These are very high energy photons. β −or e − β +or BETA: ELECTRONS, POSITRONS An5ma4er electrons (called e + positrons) can also shoot out. These are also called BETA PARTICLES. α ALPHA PARTICLES: These are clumps of TWO NEUTRONS AND TWO PROTONS – just like a helium nucleus. Alpha par5cle α Two protons emi4ed from nucleus (and two neutrons), which CHANGES THE TYPE OF ATOM (causing a change of Z  ­2) Summary of emission Binding Energy – “pulls” on a system, the direc5on of spontaneous change Another way to understand WHY some atoms decay is in terms of ENERGY. Physical systems are “pulled” towards a state that increases their binding energy. Binding Energy – “pulls” on a system, the direc5on of spontaneous change Another way to understand WHY some atoms decay is in terms of ENERGY. Physical systems are “pulled” towards a state that increases their binding energy. EXAMPLE: When a BALL rolls DOWN a HILL, the lower it gets, the greater the gravita5onal binding energy. Rolling happens spontaneously. Binding Energy – “pulls” on a system, the direc5on of spontaneous change Another way to understand WHY some atoms decay is in terms of ENERGY. Physical systems are “pulled” towards a state that increases their binding energy. EXAMPLE: When a BALL rolls DOWN a HILL, the lower it gets, the greater the gravita5onal binding energy. Rolling happens spontaneously. EXAMPLE: When there’s a VACANCY in a lower atomic orbital, an electron from farther out increases the binding energy by filling the lower orbital. Transi5on down happens spontaneously. Ball on a Hill – pulled towards greater binding energy Gravity Max binding energy (with Earth, gravity) Bowl ­shaped “hill” Ball on a Hill – pulled towards greater binding energy A strong enough barrier can prevent ball from geong to bo4om, but the pull is s5ll there. Ball on a Hill – pulled towards greater binding energy Mud, or other par5al barrier can be an obstacle and slow down the ball’s trajectory to the bo4om. Ball on a Hill – pulled towards greater binding energy We’ll learn how to calculate binding energy for an atom later. For now, let’s see how RADIOACTIVE DECAY IS LIKE A BALL ROLLING DOWN A HILL. (max binding energy) Like rolling balls, atoms have “pull” to move towards having the larger binding energy of iron. (Barriers can prevent geong there!) Like rolling balls, atoms have “pull” to move towards having the larger binding energy of iron. (Barriers can prevent geong there!) This is just an analogy, which breaks down if taken too literally. What really counts is the binding energy per nucleon (protons and neutrons). And, a helium atom, for example, can’t really “roll” into iron without more nucleons present – but iron is where nucleons would find their lowest binding energy per nucleon. Like rolling balls, atoms have “pull” to move towards having the larger binding energy of iron. (Barriers can prevent geong there!) This is just an analogy, which breaks down if taken too literally. What really counts is the binding energy per nucleon (protons and neutrons). And, a helium atom, for example, can’t really “roll” into iron without more nucleons present – but iron is where nucleons would find their lowest binding energy per nucleon. “mix” hydrogen and oxygen in a bowl, and H20 results with the lowest binding energy. “mix” the atoms of the periodic table (very hard!!) and MORE iron will result Like rolling balls, atoms have “pull” to move towards having the larger binding energy of iron. (Barriers can prevent geong there!) Iron is the atom with the GREATEST binding energy “per nucleon” Like rolling balls, atoms have “pull” to move towards having the larger binding energy of iron. (Barriers can prevent geong there!) The greater the obstacle, the longer it takes for the radioac5ve decay Normally, this plot is INVERTED….. Iron ­56 is not merely stable; no re ­distribu-on of its protons and neutrons would lead to greater binding energy per nucleon Iron ­56 is not merely stable; no re ­distribu-on of its protons and neutrons would lead to greater binding energy per nucleon Fusion: small atoms come together to make larger ones Fission: large atoms break apart A radioac5ve pathway from uranium to lead Define variables used in radioac5vity: A = " activity", units are decays/sec N = number of (remaining) radioactive atoms λ = decay constant Different for each radioac5ve isotope Basic equa5ons of radioac5vity: ΔN A=− Δt A = λN activity λ = decay constant A = ( Ainitial )e (0.693) T1 = 2 λ − λt decay equation half − life Radioac5ve decay is loosely analogous to popping popcorn… You never know which kernel will go pop, and there’s only an AVERAGE 5me for half of a batch to top (half ­life) A = ( Ainitial )e − λt decays/sec € € decay equation A = ( Ainitial )e − λt decay equation decays/sec Radioac5vity drops to half ager 10 seconds, which is this isotopes “half life”. A = decays/sec € € A = ( Ainitial )e − λt decay equation decays/sec Radioac5vity drops to half ager 10 seconds, which is this isotopes “half life”. A = decays/sec € € Drops by HALF again, in another 10 sec. A = ( Ainitial )e − λt decay equation decays/sec Radioac5vity drops to half ager 10 seconds, which is this isotopes “half life”. A = decays/sec € € Drops by HALF again, in another 10 sec. Yes, this is on the MCAT Half life examples: Most of Earth’s internal heat comes from three decays; here are their half ­lives: Potassium 40 half ­life = 1.25 billion yrs Thorium 232 half ­life = 14 billion yrs (about age of Universe) Uranium 238 half ­life = 4.5 billion yrs (about age of Earth) Half life examples: Most of Earth’s internal heat comes from three decays; here are their half ­lives: Potassium 40 half ­life = 1.25 billion yrs Thorium 232 half ­life = 14 billion yrs (about age of Universe) Uranium 238 half ­life = 4.5 billion yrs (about age of Earth) About what frac+on of Earth’s original U ­238 would you expect to find today in rocks? Half life examples: Most of Earth’s internal heat comes from three decays; here are their half ­lives: Potassium 40 half ­life = 1.25 billion yrs Thorium 232 half ­life = 14 billion yrs (about age of Universe) Uranium 238 half ­life = 4.5 billion yrs (about age of Earth) About what frac+on of Earth’s original U ­238 would you expect to find today in rocks? Since the Earth is about 4.5 billion years old, Earth has lost about HALF of its original U238 Start with 20 radioac5ve atoms Frac5on remaining of original radioac5ve material Exponen5al Decay Time measured in half lives Positron Emission Tomography – PET Scan The positron, e+, is made of ANTIMATTER! When it meets an e ­ they BOTH disappear into a BURST of LIGHT: Two gamma ray photons. Positron Annihila+on The positron, e+, is made of ANTIMATTER! When it meets an e ­ they BOTH disappear into a BURST of LIGHT: Two gamma ray photons. That 180 is important – they come out on a LINE Positron Annihila+on PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. PET Scan of mouse’s brain tumor Pair of gamma rays emerge from tracer within tumor PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. FDG decays, emits a positron e+ PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. FDG decays, emits a positron e+ e+ QUICKLY annihilates with nearby e ­ PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. FDG decays, emits a positron e+ e+ QUICKLY annihilates with nearby e ­ PAIR of gamma rays detected by scanner. PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. FDG decays, emits a positron e+ e+ QUICKLY annihilates with nearby e ­ PAIR of gamma rays detected by scanner. Background NOISE rejected because it’s not in pairs! PET Scan A radioac5ve sugar (FDG) preferen5ally collects in higher ­metabolism 5ssue. FDG decays, emits a positron e+ e+ QUICKLY annihilates with nearby e ­ PAIR of gamma rays detected by scanner. Background NOISE rejected because it’s not in pairs! Timing and line ­of ­emission determine where tracer accumulated PET Scan PET Scan About 5 mm resolu5on STUDENTS: what factors might determine the RESOLUTION of PET scan? PET Scan About 5 mm resolu5on  ­Detector size and geometry  ­Energy of positron radia5on, since low energy travels farther before annihila5on  ­Density of 5ssue STUDENTS: what factors might determine the RESOLUTION of PET scan? ...
View Full Document

Ask a homework question - tutors are online