To be more clear, deuterium contains 1 proton and 1 neutron in the nucleus, and tritium contains 1 proton and 2 neutrons in its nucleus. Both isotopes behave similarly to ordinary hydrogen, as this chemical behavior is mostly driven by the atomic electrons.
Note: The 226 refers to the atomic weight, which is the equal to the number of protons plus neutrons
Note that in beta decay, the atomic mass not change, since the neutron and proton have nearly the same mass…
So, lifetime is just another measure of how quickly the particles will decay away. If the lifetime is short, the particles will decay away quickly. If the lifetime is long (like some U-238 isotopes), it will be around for a very long time!
* In the context of talking about the lifetime, we are implying that we have a large sample of the substance containing many radioactive atoms. The lifetime represents the fraction pf atoms which will have decayed. Unfortunately, we cannot say exactly which ones will have decayed…
Note: The number “e” is very common in math and physics. It has the value: e = 2.718
But, what if we only have 1 particle before us? What can be said about it’s decay ? In this case, the radioactive decay law gives the probability that this particle will have NOT decayed (I.e., it survived without decaying) after some time. Survival Probability = N / N 0 = e -t/ So, the probability that a single unstable particle will survive after 1 lifetime is 37%; 5% chance it’ll be around after 2 lifetimes; 2% chance it’ll be around after 3 lifetimes, and so on… Now, sometimes, we want to know the probability for a certain particle to decay. This is simply obtained by saying: Decay Probability = 1.0 – (Survival Probability)
FUNDAMENTAL FORCES OF NATURE Familiar Forces Tension Forces Ask a student to hold one end of a piece of string in their hand, while you pull on the other end. Test your strength on a Newton spring balance. The tension (stretching) force is along the string and away from the support point. Compression Forces Push (gently) against the palm of someone's hand with a ruler. The compression (squashing) force is along the ruler and towards the support point. When a ruler is flexed so that it curves downward at its midpoint, the timber fibres on the ‘inside’ of the curve will be in compression. The fibres on the ‘outside’ of the curve will be in tension. The same thing happens in a concrete bridge or the lintel over a window or door, even though it is not obvious to the eye. That’s why it’s necessary to place reinforcing steel bars in the section of a concrete beam which is in tension, since concrete is weak in tension but reasonably strong in compression. Friction Forces Everyone is familiar with how difficult it is to walk on icy surfaces. Most people, at some time or other, have slipped at the kitchen sink because of water spillage. Many have experienced a nasty fright when the car in which they were travelling skidded. Try pushing the computer mouse pad along the table. Friction is a contact force between surfaces whose critical importance becomes obvious only when it’s absent. Reaction Forces When you push against a wall, the wall pushes back. When a lift travels from the top storey of a tall building, you experience a mild version of weightlessness, as the upward reaction exerted by the lift floor on you is momentarily reduced. On the other hand, you experience a momentary weight increase when the lift takes off from the ground. Seatbelts are worn in cars at all times and in aeroplanes at take-off and landing to provide reaction forces against the forces arising from accelerations. The Four Fundamental Forces of Nature The Gravitational Force When a baby starts to play by dropping objects out of its pram, it has begun its journey as an experimental physicist. Familiarity hides the wondrous and unusual nature of this force from our close scrutiny. This force intrigued the ancient Greeks, who claimed that heavier objects fell towards the ground faster than lighter ones. It is claimed that Galileo showed by experiment that two objects, regardless of their weights, would hit the ground simultaneously if dropped from identical heights. A careful reading of Galileo's experiments shows that he was well aware of the effects of air resistance on falling objects. Based on the classical wisdom of the Greek Philosophers, especially Plato and Aristotle, the Earth was the place where change occurred. In contrast the Heavens were eternal and unchanging. When Newton observed the 'apple fall from the tree', he had a brilliant insight. In his own words, 'I began to think of gravity extending to ye orb of the moon ', Newton proceeded to show by calculation that the gravitational force which caused the apple to fall to the ground was the same as the force that caused the moon to accelerate towards the Earth. He showed, on the basis of known measurements, that , where is the acceleration experienced by the moon due to the Earth's gravitational pull and g is the acceleration due to gravity at the Earth's surface. He then proceeded to compute the ratio on the basis of the 'inverse square law' and obtained the same answer. The hammer blow to the classical view was his derivation of the elliptical orbits of the planets around the Sun from the same inverse square law of gravitational force. Every particle of matter in the universe attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of their distances apart. In symbols F is the gravitational force; G is the universal gravitational constant; m 1 and m 2 are the particle masses and d is the distance between their centres of mass. Newton believed the force was proportional to the mass of each particle, because the force on a falling body is proportional to its mass. This relationship is known as Newton’s law of gravitation. The law applies to particles or objects whose dimensions are very small compared with the other distances involved. Newton was able to show that even an object as big as the Earth could be viewed as a uniform sphere with all the mass concentrated at its centre point. The gravitational force is a very small force. It is a very difficult force to detect between two 1 kg masses 1 m apart. In this case it is in fact numerically equal to G , with a value of N. Some appreciation of just how tiny this is can be gauged by comparison with the force on a falling apple, which is roughly 1 N. It is so small that it can be ignored inside atoms. However, it dominates everyday life due to the close proximity of the huge mass of the Earth and because it is only attractive. Its range is infinite. Newton's law of gravitation explains how a body falls and how the planets move around the Sun, but leaves unexplained why these events happen as they do. The gravitational force pulls objects towards each other, even though they are not in physical contact. Modern physics interprets this action at a distance as arising from an exchange of particles between the objects experiencing the force. In the case of the gravitational force the exchange particle is called the graviton . The graviton is postulated to exist, but has not been discovered. The gravitational force is a fundamental force because it operates between any two elementary particles. The Electromagnetic Force Experiments show that, sometimes, after any two different materials are rubbed together they exert forces on each other. Each has acquired an 'electric charge'. Furthermore, experiments show that there are two kinds of charge. The two kinds tend to cancel one another out and in this respect are opposite. Hence one kind is called positive and the other kind is called negative. Polythene rubbed with wool acquires a negative charge , whereas perspex (cellulose acetate) rubbed with wool acquires a positive charge. The force between two point charges is proportional to the product of the charges and is inversely proportional to the square of their distance apart. In symbols where F is the force, Q 1 and Q 2 are the charges and d is the separation distance. for air or vacuum. This relationship is called Coulomb’s law. Moving charges experience a force in a magnetic field and also create (induce) magnetic fields. The combined effect (if applicable) of the magnetic force and the coulomb electrostatic force is called the electromagnetic force. We do not directly experience the strength of the electrostatic force as individuals. The delicate balance between the negative electrons and the positive protons in our constituent atoms prevents such an experience. Suppose however that 0.1% of someone's electrons were transferred to someone else. The consequent force of attraction that these people would feel at a distance of 1 m apart can be found by applying Coulomb’s law. For simplicity, suppose the mass of each person is 50 kg and that each person is composed entirely of C-12 atoms. Now 12 grams of carbon contains electrons [No. of electrons in a carbon atom × No. of carbon atoms in one mole]. Hence the total number of electrons in each person is . Thus the number of electrons moved from one person to the other is . The force of attraction is N. This force is approximately equal to a thousandth part of the weight of the earth. It is also instructive to compare the eleectrostatic and gravitational attractions between a proton (charge +e and mass kg) and an electron (charge -e C and mass kg) placed 1 metre apart. F e = electric attraction N F g = gravitational attraction N Hence . The electromagnetic force acts between all charged particles. Its range is infinite. It is the force that binds atoms and molecules together. It is responsible for tension, compression, friction and reaction forces at the atomic level. Like gravity, it acts at a distance, with the photon acting as the exchange particle. The Strong Nuclear Force This is the very strong attractive force between nucleons, which holds the atomic nucleus together against the repulsive electrostatic forces between protons. It is also called the strong interaction. Its existence was confirmed by the discovery of the neutron. The strong force acts over a very short range. If its effects went much outside the nuclear surface, it would not be possible to explain Rutherford's alpha-particle scattering experiment solely in terms of electrostatic repulsion. In the range of internucleon separation of about 1 to 3 fm it is strongly attractive, but more or less disappears beyond 3 fm. (m) [1 fm = 1 femtometre] At distances of less than 1 fm the force must be sufficiently repulsive to prevent the nucleus collapsing. The strong nuclear force acts at a distance, as was the case with the gravitational and electrostatic forces. Imagine the nucleons as a group of dancers. If they form a ring by interlocking hands around their waists, they can continue to dance quite comfortably provided they stay within limits. If they try to pull apart, the 'force' holding them together gets stronger; if they get too close together they can no longer dance comfortably. The Weak Nuclear Force (The Weak Interaction) In 1930, on the basis of energy and momentum conservation, Pauli proposed the existence of a third particle to explain the range of energies shown by the electrons in beta emission. He offered a crate of champagne to the first person to prove the existence of this particle, which was christened the neutrino by the Italian physicist Enrico Fermi in a jocular response to a journalist's question about Chadwick's discovery of the neutron. The neutrino proved extremely elusive. Cowan and Reines finally found it in 1956. Its existence implies that there is a fourth distinct force in nature. Its interaction with matter is so rare and tenuous that this interaction cannot be explained in terms of any of the other three fundamental forces. This fourth force is called the weak nuclear force or the weak interaction. It is intermediate in strength between the gravitational and electromagnetic forces. It has a range of less than 10 -2 fm. This force also acts at a distance. This weak interaction, or force, is involved when a neutron decays to a proton, electron, and an antineutrino in the process called beta decay. Comparison of the Four Fundamental Forces Force Relative Strength Range Action Gravitational 1 all particles Weak Nuclear 10 23 10 -18 m all particles Electromagnetic 10 36 charged particles Strong Nuclear 10 38 10 -15 m protons, neutrons
Modern Physics MOHAMMAD IMRAN AZIZ Assistant Professor PHYSICS DEPARTMENT SHIBLI NATIONAL COLLEGE, AZAMGARH (India). [email_address]
Use an interferometer to measure the speed of light at different times of the year
Since the earth rotates on its axis and revolves around the sun, we have all kinds of chances to observe different motions of the earth w.r.t. the ether
Michelson-Morley We get an interference pattern by adding the horizontal path light to the vertical path light. If the apparatus moves w.r.t. the ether, then assume the speed of light in the horizontal direction is modified. Then rotate the apparatus and the fringes will shift. [email_address]
It is clear that electrons are components of atoms
That must mean there is some positive charge somewhere inside the atom so that atoms remain neutral
The earliest model was called the “plum pudding” model
Plum Pudding Model We have a blob of positive charge and the electrons are embedded in the blob like currants in a plum pudding. However, people thought that the electrons couldn’t just sit still inside the blob. Electrostatic forces would cause accelerations. How could it work? [email_address]
Rutherford’s model allowed calculating the radius of the seat of positive charge in order to produce the observed angular distribution of rebounding alpha particles
Remarkably, the size of the seat of positive charge turned out to be about 10 -15 meters
Atomic spacings were about 10 -10 meters in solids, so atoms are mostly empty space
Rutherford Scattering From the edge of the atom, the nucleus appears to be 1 meter across from a distance of 10 5 meters or 10 km. Translating sizes a bit, the nucleus appears as an orange viewed from a distance of just over three miles!!! This is TINY!!! [email_address]
Rutherford Scattering Rutherford assumed the electrons must be in some kind of orbits around the nucleus that extended out to the size of the atom. Major problem is that electrons would be undergoing centripetal acceleration and should emit EM waves, lose energy and spiral into the nucleus! Not very satisfactory situation! [email_address]
Classical picture: oscillating electromagnetic field causes oscillations in positions of charged particles, which re-radiate in all directions at same frequency as incident radiation. No change in wavelength of scattered light is expected
Compton’s explanation: collisions between particles of light (X-ray photons) and electrons in the material
[email_address] Oscillating electron Incident light wave Emitted light wave θ Before After Electron Incoming photon scattered photon scattered electron
Compton scattering 4 Conservation of energy Conservation of momentum From this derive change in wavelength: [email_address] θ Before After Electron Incoming photon scattered photon scattered electron
Originally performed by Young (1801) to demonstrate the wave-nature of light. Has now been done with electrons, neutrons, He atoms,…
D d Detecting screen y Alternative method of detection: scan a detector across the plane and record number of arrivals at each point Expectation: two peaks for particles, interference pattern for waves [email_address]
Maxima when: Position on screen: D >> d use small angle approximation So separation between adjacent maxima: Fringe spacing in double slit experiment [email_address] d θ D y
C. Jönsson (Tübingen, Germany, 1961) showed double-slit interference effects for electrons by constructing very narrow slits and using relatively large distances between the slits and the observation screen.
experiment demonstrates that precisely the same behavior occurs for both light (waves) and electrons (particles).
Neutrons, A Zeilinger et al. Reviews of Modern Physics 60 1067-1073 ( 1988) He atoms: O Carnal and J Mlynek Physical Review Letters 66 2689-2692 ( 1991) C 60 molecules: M Arndt et al. Nature 401, 680-682 ( 1999) With multiple-slit grating Without grating Results on matter wave interference Interference patterns can not be explained classically - clear demonstration of matter waves [email_address] Fringe visibility decreases as molecules are heated. L. Hackermüller et al. , Nature 427 711-714 ( 2004)
Try to determine which slit the electron went through.
Shine light on the double slit and observe with a microscope. After the electron passes through one of the slits, light bounces off it; observing the reflected light, we determine which slit the electron went through.
The photon momentum is:
The electron momentum is:
The momentum of the photons used to determine which slit the electron went through is enough to strongly modify the momentum of the electron itself—changing the direction of the electron! The attempt to identify which slit the electron passes through will in itself change the diffraction pattern!
Need ph < d to distinguish the slits. Diffraction is significant only when the aperture is ~ the wavelength of the wave. [email_address]
Discussion/interpretation of double slit experiment
Reduce flux of particles arriving at the slits so that only one particle arrives at a time. -- still interference fringes observed!
Wave-behavior can be shown by a single atom or photon.
Each particle goes through both slits at once.
A matter wave can interfere with itself .
Wavelength of matter wave unconnected to any internal size of particle -- determined by the momentum
If we try to find out which slit the particle goes through the interference pattern vanishes!
We cannot see the wave and particle nature at the same time.
If we know which path the particle takes, we lose the fringes .
Richard Feynman about two-slit experiment: “…a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality it contains the only mystery.” [email_address]
orbiting electron behaves like current loop magnetic moment interaction energy = μ · B (both vectors!)
loop current = -ev/(2 π r)
magnetic moment μ = current x area = - μ B L/ħ μ B = e ħ/2m e = Bohr magneton
interaction energy = m μ B B z (m = z –comp of L)
[email_address] e I A
Splitting of atomic energy levels Predictions: should always get an odd number of levels. An s state (such as the ground state of hydrogen, n= 1, l =0, m =0) should not be split. Splitting was observed by Zeeman (2l+1) states with same energy: m=-l,…+l (Hence the name “magnetic quantum number” for m .) B ≠ 0: (2l+1) states with distinct energies m = 0 m = -1 m = +1 [email_address]
Radiation Radiation : The process of emitting energy in the form of waves or particles. Where does radiation come from? Radiation is generally produced when particles interact or decay. A large contribution of the radiation on earth is from the sun (solar) or from radioactive isotopes of the elements (terrestrial). Radiation is going through you at this very moment! http://www.atral.com/U238.html
Isotopes What’s an isotope? Two or more varieties of an element having the same number of protons but different number of neutrons. Certain isotopes are “unstable” and decay to lighter isotopes or elements. Deuterium and tritium are isotopes of hydrogen. In addition to the 1 proton, they have 1 and 2 additional neutrons in the nucleus respectively*. Another prime example is Uranium 238, or just 238 U.
These particles generally come from the nuclei of atomic isotopes which are not stable .
The decay chain of Uranium produces all three of these forms of radiation.
Let’s look at them in more detail…
Alpha Particles ( ) Radium R 226 88 protons 138 neutrons Radon Rn 222 Note: This is the atomic weight, which is the number of protons plus neutrons 86 protons 136 neutrons + n n p p He) 2 protons 2 neutrons The alpha-particle is a Helium nucleus . It’s the same as the element Helium , with the electrons stripped off !
Beta Particles ( ) Carbon C 14 6 protons 8 neutrons Nitrogen N 14 7 protons 7 neutrons + e - electron (beta-particle) We see that one of the neutrons from the C 14 nucleus “converted” into a proton, and an electron was ejected. The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred: n p + e ( + Yes, the same neutrino we saw previously
Gamma particles ( ) In much the same way that electrons in atoms can be in an excited state , so can a nucleus. Neon Ne 20 10 protons 10 neutrons (in excited state) 10 protons 10 neutrons (lowest energy state) + gamma Neon Ne 20 A gamma is a high energy light particle . It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.
Gamma Rays Neon Ne 20 + The gamma from nuclear decay is in the X-ray/ Gamma ray part of the EM spectrum (very energetic!) Neon Ne 20
How do these particles differ ? * m = E / c 2 Particle Mass* (MeV/c 2 ) Charge Gamma ( ) 0 0 Beta ( ) ~0.5 -1 Alpha ( ) ~3752 +2
If I had 1000 free neutrons in a box, after 14.7 minutes some number of them will have decayed.
The number remaining after some time is given by the radioactive decay law
N 0 = starting number of particles = particle’s lifetime This is the “exponential”. It’s value is 2.718, and is a very useful number. Can you find it on your calculator?
Lifetime (II) Note by slight rearrangement of this formula: Fraction of particles which did not decay : N / N 0 = e -t/ After 4-5 lifetimes, almost all of the unstable particles have decayed away! # lifetimes Time (min) Fraction of remaining neutrons 0 0 1.0 1 14.7 0.368 2 29.4 0.135 3 44.1 0.050 4 58.8 0.018 5 73.5 0.007
If the particle’s lifetime is very short, the particles decay away very quickly.
When we get to subatomic particles, the lifetimes are typically only a small fraction of a second!
If the lifetime is long (like 238 U) it will hang around for a very long time!
Lifetime (IV) What if we only have 1 particle before us? What can we say about it? Survival Probability = N / N 0 = e -t/ Decay Probability = 1.0 – (Survival Probability) # lifetimes Survival Probability (percent) Decay Probability = 1.0 – Survival Probability (Percent) 1 37% 63% 2 14% 86% 3 5% 95% 4 2% 98% 5 0.7% 99.3%
In Nuclear Reactions momentum and mass-energy is conserved – for a closed system the total momentum and energy of the particles present after the reaction is equal to the total momentum and energy of the particles before the reaction
In the case where an alpha particle is released from an unstable nucleus the momentum of the alpha particle and the new nucleus is the same as the momentum of the original unstable nucleus
Conservation Laws [email_address]
Neutrino must be present to account for conservation of energy and momentum
Large variations in the emission velocities of the particle seemed to indicate that both energy and momentum were not conserved.
This led to the proposal by Wolfgang Pauli of another particle, the neutrino, being emitted in decay to carry away the missing mass and momentum.
The neutrino (little neutral one) was discovered in 1956.
Wolfgang Pauli __ [email_address]
Calculate the energy released in the reaction 1.008665 u 1.007825 u 0.0005486 u 1 u = 1 J = __ kg eV [email_address]
Mass difference Calculation kg kg u [email_address]
It has been found by experiment that the emitted beta particle has less energy than 0.272 MeV Neutrino accounts for the ‘missing’ energy Calculation J J eV MeV [email_address]
History of search for basic building blocks of nature
Earth, Air, Fire, Wate r
By 1900, nearly 100 elements
By 1936, back to three particles: proton, neutron, electron
Thomson (1897): Discovers electron [email_address]
Leptons Indivisible point objects Not subject to the strong force produced in radioactive decay Q = -1e almost all trapped in atoms Q= 0 all freely moving through universe _ [email_address]
Baryons Mesons Subject to all forces mass between electron and proton e.g. protons, neutrons and heavier particles Composed of three quarks Composed of quark-antiquark pair Subject to all forces [email_address]
J ust as the equation x 2 =4 can have two possible solutions (x=2 OR x=-2), so Dirac's equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy. Dirac interpreted this to mean that for every particle that exists there is a corresponding antiparticle, exactly matching the particle but with opposite charge. For the electron, for instance, there should be an "antielectron" called the positron identical in every way but with a positive electric charge. [email_address]
History of Antimatter 1928 Dirac predicted existence of antimatter 1932 antielectrons (positrons) found in conversion of energy into matter 1995 antihydrogen consisting of antiprotons and positrons produced at CERN In principle an antiworld can be built from antimatter Produced only in accelerators and in cosmic rays [email_address]