IB+DP+Topic+12+Quantum+and+nuclear+physics+(AHL)

12.1 The interaction of matter with radiation [|Ultrafast Electron Diffraction:] [|How It Works][|SLAC National Accelerator Laboratory] Published on 5 Aug 2015 || media type="youtube" key="YYG8nv6vzoY" width="560" height="315" [|The Weird Quantum World] (11 of 15) [|Science and Technology Facilities Council] Published on 1 Mar 2008 ||
 * media type="youtube" key="XVvhQIlCft8" width="560" height="315"

Essential idea: The microscopic quantum world offers a range of phenomena, the interpretation and explanation of which require new ideas and concepts not found in the classical world.

Nature of science: Observations: Much of the work towards a quantum theory of atoms was guided by the need to explain the observed patterns in atomic spectra. The first quantum model of matter is the Bohr model for hydrogen. (1.8) Paradigm shift: The acceptance of the wave–particle duality paradox for light and particles required scientists in many fields to view research from new perspectives. (2.3)

Understandings: • Photons • The photoelectric effect • Matter waves • Pair production and pair annihilation • Quantization of angular momentum in the Bohr model for hydrogen • The wave function • The uncertainty principle for energy and time and position and momentum • Tunnelling, potential barrier and factors affecting tunnelling probability

Theory of knowledge: • The duality of matter and tunnelling are cases where the laws of classical physics are violated. To what extent have advances in technology enabled paradigm shifts in science?

Utilization: • The electron microscope and the tunnelling electron microscope rely on the findings from studies in quantum physics • Probability is treated in a mathematical sense in Mathematical studies SL subtopics 3.6–3.7

Applications and skills: • Discussing the photoelectric effect experiment and explaining which features of the experiment cannot be explained by the classical wave theory of light • Solving photoelectric problems both graphically and algebraically • Discussing experimental evidence for matter waves, including an experiment in which the wave nature of electrons is evident • Stating order of magnitude estimates from the uncertainty principle

Guidance: • The order of magnitude estimates from the uncertainty principle may include (but is not limited to) estimates of the energy of the ground state of an atom, the impossibility of an electron existing within a nucleus, and the lifetime of an electron in an excited energy state • Tunnelling to be treated qualitatively using the idea of continuity of wave functions

Aims: • Aim 1: study of quantum phenomena introduces students to an exciting new world that is not experienced at the macroscopic level. The study of tunneling is a novel phenomenon not observed in macroscopic physics. • Aim 6: the photoelectric effect can be investigated using LEDs • Aim 9: the Bohr model is very successful with hydrogen but not of any use for other elements

Data booklet reference:

[|What Is Something?] [|Kurzgesagt – In a Nutshell] Published on 23 Dec 2015

EXERCISE 1: What is the energy of photon of blue light of wavelength 470 nm, in Joules and eV ? SOLUTION 1: E = hc / l = ( 6.63 x 10 -34 Js x 3 x 10 8 m/s ) / 470 nm

Photoelectric effect
Effect 1. Below certain threshold frequency f o, no electrons are emitted. 2. Increase in intensity of light has no effect on E k of electrons. 3. Above f o, E k of electrons__ is proportional to __ the frequency. Reasons 1. Light is __**quantized**__ ( photons have E = hf ) 2. Electrons trapped in metal (Zinc) need a certain energy in order to be ejected. 3. f [ phi] __**Work function**__ ( measure in electron volt ) = energy needed to eject electrons. Image taken from K.A.Tsokos IB Dploma 6th edition p.485 hf = f + KE max KE max = hf - f The photoelectric effect depends on frequency. High frequency light eject electrons while low frequency light does not eject electrons. The photoelectric effect depends on intensity. More intensity light for same frequency, when it is greater than threshold frequency, ejects more electrons with the same kinetic energy. [|Photoelectric effect simulation] from www.walter-fendt.de

media type="custom" key="29634357"[|Photoelectric effectt] Phet simulation www.phet.colorado.edu You can make a circuit to stop photoelectrons. Stopping voltage Vs is the terminal p.d. that is needed in order to stop photoelectrons. Image taken from K.A.Tsokos IB Dploma 6th edition p.485 hf = f[ phi] + E max , E max (J) = hf - f (J) E max (J) { = eVs } = hf - f { =hf o } [All in Joules] Vs = (h/e)f - f [ All in eV]

h: constant f: frequency of incoming light (Hz) f o : threshold frequency ( Hz ) j : Work funtion (eV) Emax: maxium kinetic energy of electrons (eV) e: charge (C) Vs : stopping voltage (V)

Matter such as electrons can be diffracted through small gaps just as waves can.
 * Matter Waves**

**__De Broglie's wavelength for matter__**
E = hf, c = fl and E = hc / l

In terms of wavelength l = hc / E

E = mc 2 so l = hc / mc 2  = h / mc

For matter, mass moves with speed v, not c, and thus

l = h/mv = h / p

PRACTICE 1: What would be the electron wavelength if we were to accelerate an electron through 1000 Volts ? SOLUTION 1: Loss of electric potential energy = gain kinetic energy

eV = p 2 / 2m ( l = h/p )

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">eV = h 2 / ( 2m <span style="font-family: Symbol,sans-serif;">l 2 )

<span style="font-family: Symbol,sans-serif; font-size: medium;">l <span style="font-family: &#39;Times New Roman&#39;; font-size: 12.8px; vertical-align: super;">2 = <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;"> h <span style="font-family: &#39;Times New Roman&#39;; font-size: 12.8px; vertical-align: super;">2 <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">/ ( 2m e V )

<span style="font-family: Symbol,sans-serif;">l = ( 6.63 x 10 -34 ) / root <span style="font-family: Symbol,sans-serif;">[ 2 ( 9.1 x 10 -31 kg ) (1.6 x 10 -19 ) ( 1000 v)<span style="font-family: Symbol,sans-serif;"> ]

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;"><span style="font-family: Symbol,sans-serif;">l = 3.9 x 10 -11 <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;"> m

PRACTICE 2: D Which particle(s) does the De Broglie hypothesis apply to? A. Nucleons only B. Electrons only C. Photons only D. All particles

PRACTICE 3: A Use equation of m p v p = m<span style="font-family: Symbol,sans-serif; font-size: 9.1px;">a v<span style="font-family: Symbol,sans-serif; font-size: 9.1px; vertical-align: sub;">a PRACTICE 4: A PRACTICE 5: D Use equation of E K = P 2 /2m, p = root [ 2mqv ]

1)ELECTRON DIFFRACTION EXPERIMENT An electron ‘wave’ is passed through a gap of the same order as its wavelength. The electron waves can then be projected onto a screen where constructive interference can be seen.

Electron diffraction experiment image from www.schoolphysics.co.uk As the potential difference was increased, the rings became smaller, and this is the same as we see with diffraction of light or water waves. Electron microscopes use the wave properties of high energy electrons to make image of smaller objects. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Waves cannot resolve anything smaller than their wavelength. As electron waves can have smaller wavelengths than visible light, they can provide image of smaller objects. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Watch the video clip at [|electron diffraction] National STEM centre Published on 18 Dec 2014

**<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Atomic models **
We have already discussed Rutherford’s model of atomic structure, however it is important to acknowledge other atomic models such as:

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">1)Bohr Model <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;"> An electron does not radiate energy when in a stable orbit and the only stable orbits possible for an electron are ones where the angular momentum of the orbit is an integral multiple of ( h / 2π ): <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">mvr = n ( h / 2π ) 2 π r = nh / mv = n <span style="font-family: Symbol,sans-serif;">l <span style="font-family: arial,helvetica,sans-serif; font-size: 13px;">The allowed orbits in the Bohr model of hydrogen are those for which an integral number of electron wavelengths fit on the circumference of the orbit. The electron wave is a standing wave on the circumference. [|Bohr electron model diagram] from courses.lumenlearning.com

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Energy of the **' n** ** th **<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">**'** orbital
<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Angular momentum (L) = mvr = mass of electron x velocity x radius n = orbital number h = planck’s constant (6.63 x 10 -34 Js)

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">The energy of an orbit is proportional to -1 / n 2 <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">:
 * E = - 13.6 / n 2 (eV)**
 * [[image:Hydrogen energy spectrum in orbit.PNG width="549" height="523"]]

[|Electron transitions] for Bohr model Hydrogen atom ||

[|Electron transitions] for Hydrogen atom || <span style="background-image: url(">[|Spectral series for Bohr model of Hydrogen atom] ||

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">2)Schrodinger Model The wavefunction provides a way of working out the probability of finding an electron at a particular radius. P (r) = <span style="font-family: Symbol,sans-serif;">Y 2 <span style="font-family: Symbol,sans-serif;">D V <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">This equation represent the probability of finding an electron in a small volume of space.

Matter waves describe probability of finding electrons in different places. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Intensity is a measure of probability. They are proportional to each other. Probability is proportional to the squared value of amplitude.

<span style="font-family: &#39;Times New Roman&#39;;">Heisenberg's uncertainty principle
<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Identifies a fundamental limit to the possible accuracy of any physical measurement. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Heisenberg showed that it is impossible to measure exactly the position AND momentum of a particle simultaneously. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">The more precisely the position is determined, the less precisely the momentum is known at that instant, and vice versa. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Position and momentum and linked variables so are called conjugate quantities. <span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">x <span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">p __>__ h / 4 <span style="font-family: Symbol,sans-serif;">p

<span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">x: uncertainty on position/ experimental uncertainty in the measurement of location <span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">p: uncertainty on momentum(speed)

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Energy and time are also conjugate quantities. Therefore: <span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">E <span style="font-family: Symbol,sans-serif; font-size: medium;">D <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">t __>__ h / 4 <span style="font-family: Symbol,sans-serif; font-size: medium;">p <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">ΔE = uncertainty in energy, Δt = uncertainty in time

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">The uncertainty principle now showed that we cannot know the precise position and momentum of a particle at any given time, its future can never be determined precisely. <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">The best we can do is work out a range of possibilities.

EXAMPLE 1: The position of a proton is measured with an accuracy of + 1.0 x 10 -11 m. What is the minimum uncertainty in the proton’s position 1.0 s later?

SOLUTION 1: Δx Δp ≥ h / 4π where Δp = m Δv

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Δv ≥ h / 4π m Δx = 6.63 x 10-34 / 4π x ( 1.67 x 10 -27 ) x (1.0 x 10 -11 ) = 3200 m/s

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Therefore, after 1 second, the uncertainty in the position is 3200 m = 3.2 km

Tunnelling: The ability of subatomic particles to move into regions forbidden by energy conservation

**<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Modern atomic model timeline Project Homework **
<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Create a presentation explaining the quantum theories based on the atomic model timeline. Include modern atomic models of:


 * <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Niels Bohr (Planetary model of the atom [1913] ),
 * <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Arthur Compton ( Demonstration of the particle nature of E.M.radiation [1922] ),
 * <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Louis de Broglie ( Wave-particle duality [1924] ),
 * <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Erwin Schrödinger ( Schrödinger equation [1926] ),
 * <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">Werner Heisenberg ( Uncertainty principle. [1927] )

Accepting the idea of a wave particle duality and the idea of the wavefunctions for electrons in atoms, the uncertainty principle and probability fnctions and the need to explain the observed patterns in atomic spectra required scientists to open a new branch of physics, quantum physics. This led scientists in many fields to view research from new perspectives. The microscopic quantum world offers a range of phenomena, the interpretation and explanation of which require new ideas and concepts not found in the classical world (Paradigm shift).

<span style="background-color: #ffffff; color: #000000; font-family: Arial,sans-serif; font-size: 13px;">• <span style="background-color: #ffffff; font-family: arial,helvetica,sans-serif; font-size: 13px;">[ Energy of a quanta - Planck / Einstein ] //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">E = ////<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">hf // <span style="background-color: #ffffff; color: #000000; font-family: Arial,sans-serif; font-size: 13px;">• <span style="background-color: #ffffff; font-family: arial,helvetica,sans-serif; font-size: 13px;">[ Photoelectric effect - Einstein ] //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">E //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 9.1px; vertical-align: sub;">max //= hf//<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">- // f // <span style="background-color: #ffffff; font-family: Arial,sans-serif;">• [ Energy of the hytrogen atom - Bohr ] // E = // - (13.6 / // ** n ** // **2** ) eV <span style="background-color: #ffffff; color: #000000; font-family: Arial,sans-serif; font-size: 13px;">• <span style="background-color: #ffffff; font-family: arial,helvetica,sans-serif; font-size: 13px;">[ Quantization of angular momentum - Bohr, de Broglie ] //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">mvr = ////<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">nh //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;"> / 2 p  <span style="background-color: #ffffff; font-family: Arial,sans-serif;">• [ Wave function - Schrodinger ] // P // ( // r // ) = | ψ | 2 ∆ // V // <span style="background-color: #ffffff; color: #000000; font-family: Arial,sans-serif; font-size: 13px;">• <span style="background-color: #ffffff; font-family: arial,helvetica,sans-serif; font-size: 13px;">[ Heisenberg uncertainty principle ] <span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">∆ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">x //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">∆ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">p // <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">≥ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">h //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;"> / 4 p <span style="background-color: #ffffff; color: #000000; font-family: Arial,sans-serif; font-size: 13px;">• <span style="background-color: #ffffff; font-family: arial,helvetica,sans-serif; font-size: 13px;">[ Heisenberg uncertainty principle ] <span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">∆ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">E //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">∆ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">t // <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">≥ //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">h //<span style="background-color: #ffffff; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;"> / 4 p

12.2 Nuclear physics Essential idea: The idea of discreteness that we met in the atomic world continues to exist in the nuclear world as well.

Nature of science: Theoretical advances and inspiration: Progress in atomic, nuclear and particle physics often came from theoretical advances and strokes of inspiration. Advances in instrumentation: New ways of detecting subatomic particles due to advances in electronic technology were also crucial. Modern computing power: Finally, the analysis of the data gathered in modern particle detectors in particle accelerator experiments would be impossible without modern computing power. (1.8)

Understandings: • Rutherford scattering and nuclear radius • Nuclear energy levels • The neutrino • The law of radioactive decay and the decay constant

Applications and skills: • Describing a scattering experiment including location of minimum intensity for the diffracted particles based on their de Broglie wavelength • Explaining deviations from Rutherford scattering in high energy experiments • Describing experimental evidence for nuclear energy levels • Solving problems involving the radioactive decay law for arbitrary time intervals • Explaining the methods for measuring short and long half-lives

Theory of knowledge: • Much of the knowledge about subatomic particles is based on the models one uses to interpret the data from experiments. How can we be sure that we are discovering an “independent truth” not influenced by our models? Is there such a thing as a single truth?

Utilization: • Knowledge of radioactivity, radioactive substances and the radioactive decay law are crucial in modern nuclear medicine (see Physics option sub-topic C.4)

Guidance: • Students should be aware that nuclear densities are approximately the same for all nuclei and that the only macroscopic objects with the same density as nuclei are neutron stars • The small angle approximation is usually not appropriate to use to determine the location of the minimum intensity

Aims: • Aim 2: detection of the neutrino demonstrates the continuing growing body of knowledge scientists are gathering in this area of study

Data booklet reference: Published on 14 Apr 2011 || [|Rutherford scattering simulation] from Phet.colorado.edu || If the energy of the incoming particle is increased, the distance of closest approach decreases. The smallest it can get will be the radius of the nucleus. Experiments of this kind have been used to estimate the nuclear radii. The nuclear radius R depends on mass number A: <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">R : radius of nucleus <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">R 0 <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">: 1.20 x 10 -15 <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> m <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 13.3333px;"> ( Fermi radius) <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">A : nucleon number
 * media type="youtube" key="XBqHkraf8iE" width="560" height="315" || [[image:sciencelanguagegallery/Rutherford scattering sim.PNG width="473" height="320"]] ||
 * [|Rutherford Gold Foil Experiment] - Backstage Science [|BackstageScience]
 * <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">Estimating the size of a nucleus **
 * <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">R = R 0 <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> A 1/3 **

<span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">Simple energy considerations can be used to calculate the distance of closest approach of the incoming particle to the target, such as alpha particles or neutrons that are projected head on toward a stationary nucleus to determine the radius of the nucleus.The electromagnetic charge of alpha particles, however, stops them from getting close to the nucleus so alpa particles are not used to probe inside a nucleus while the electrons and neutrons will diffract around the nuclei. A minimum will be formed at an angle to the original direction:
 * <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;">Measurement of the nucleus by Electron Scattering **

<span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> **sin θ = λ / b**

<span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> where b is diameter of the diffracting object. i.e. diameter of the nucleus <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> θ is the first diffraction minimum and <span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 10pt;"> λ is the wavelength of electrons (de Broglie wavelength) [|Quantum physics base] from hyperphysics
 * [[image:sciencelanguagegallery/Rutherford scattering trajectories of alpha particles.jpg]] ||

<span style="background-color: #ffffff; color: #0c0c0c; display: block; font-family: Helvetica,Arial,sans-serif; font-size: 15px; vertical-align: baseline;"> <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;"><span style="color: #0c0c0c; font-family: Arial,sans-serif; font-size: 13.3333px;">Just like alpha particles, electrons are scattered off a nucleus, however, instead of repelling away from the nucleus, the electron and nucleus are attracted to each other. The presence of these deviations from perfect Rutherford scattering is evidence of the existence of the strong nuclear force. Electrons are used instead of alpha particles because they are not affected by the force that holds the nuclei together. <span style="font-family: Arial,sans-serif; font-size: 13.3333px;">E = pc and λ = h / p to work out the momentum and energy of the electrons.
 * Deviation from Rutherford scattering **

<span style="font-family: Arial,sans-serif; font-size: 10pt;">High energy electrons are needed so that the wavelength is about the same dimensions as of a nucleus. <span style="font-family: Arial,sans-serif; font-size: 10pt; line-height: 0px; overflow: hidden;"> <span style="font-family: Calibri,sans-serif; font-size: 12pt;">EXAMPLE 3: Calculate the radius of a nucleus when 400MeV electron beam are incident on a thin sample and made the first diffraction minimum at an angle of 35 degrees to the central position. <span style="background-color: #ffffff; color: #0c0c0c; display: block; font-family: Helvetica,Arial,sans-serif; font-size: 15px; vertical-align: baseline;"> <span style="color: #000000; font-family: arial,helvetica,sans-serif; font-size: 13px;">Aim: To define the relationship between the impact parameter D and the scattering angle //theta//<span style="font-family: Symbol,sans-serif;">, q //.// Task: Plot a graph using your data collected from simulation and draw conclusion showing the relationship below using a Rutherford scattering simulation. sin <span style="font-family: Symbol,sans-serif;">q = <span style="font-family: Symbol,sans-serif;">l / D where <span style="font-family: Symbol,sans-serif;">q is an angle where the first minimum interference formed D is the diameter of the diffracting object, i.e. the nucleus The relation between the impact parameter and the scattering angle simplifies with the use of the distance of the closest approach to a nucleus. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">The energy levels in the nucleus are higher than those of electrons but the principle remains the same: //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">When an alpha particle or gamma photon is emitted from the nucleus, only discrete energies are observed. // <span style="font-family: Calibri,sans-serif; font-size: 11pt;">These energies correspond to the difference between two **nuclear energy levels** in the same way that the photons energies correspond to the difference between two **atomic energy levels**. Beta particles are observed to have a continuous spectrum of energies. In this case, there is another particle (antineutrino) that shares the energy. The beta particle and antineutrino take varying proportions of the available energy.
 * Nuclear energy levels **

<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Wolfgang Pauli hypothesised the existence of a third particle in the products of a beta minus decay in 1933. It is needed to account for the ‘missing’ energy and momentum when analysing a decay mathematically. Calculations involving mass difference mean that we know how much energy is available for beta decay. However, most beta decays have less than half the total energy so the remaining energy must be transferred elsewhere (neutrino).
 * Neutrino**

<span style="font-family: Calibri,sans-serif; font-size: 11pt;">The neutrino (and antineutrino) must be:
 * //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">electrically neutral //
 * //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">have an extremely small mass //

<span style="font-family: Calibri,sans-serif; font-size: 11pt;">The neutrino must carry away the excess energy but is extremely hard to detect. Recently, the neutrinos and antineutrinos existence was confirmed through experimentation of the beta decay of tritium (hydrogen-3)

<span style="font-family: Calibri,sans-serif; font-size: 11pt;">**A = A** 0 <span style="font-family: Calibri,sans-serif; font-size: 11pt;"> **e** -λt <span style="font-family: Calibri,sans-serif; font-size: 11pt;">**= N** 0 <span style="font-family: Calibri,sans-serif; font-size: 11pt;"> **λ e** -λt <span style="font-family: Calibri,sans-serif; font-size: 14.6667px;">A graph of A versus N gives a straight line whose slope is the decay constant. N o : Initial mass N : Final mass T : Time it takes to have half the original mass or number of particles (N) l (decay constant) : probability of decay per unit time ( 1/s or 1/year) t : time elapsed A : activity (Bq, decays /s) <span style="font-family: Calibri,sans-serif; font-size: 14.6667px;">(A = Nλ) <span style="font-family: Calibri,sans-serif; font-size: 11pt;">N 0 <span style="font-family: Calibri,sans-serif; font-size: 11pt;"> = initial number of nuclei <span style="font-family: Calibri,sans-serif; font-size: 11pt;">A 0 <span style="font-family: Calibri,sans-serif; font-size: 11pt;"> = initial activity
 * Nuclear physics ( decay )**
 * N = N o e <span style="font-family: Symbol,sans-serif; font-size: 9.1px; vertical-align: super;">-l <span style="font-family: Arial,Helvetica,sans-serif; font-size: 70%; vertical-align: super;">t **

<span style="font-family: Calibri,sans-serif; font-size: 14.6667px; line-height: 0px; overflow: hidden;">Graphically, the gradient of a natural log (ln) of activity OR number of nuclei vs time graph will give the negative decay constant (-λ) <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 0px; overflow: hidden;"> <span style="font-family: Calibri,sans-serif; font-size: 14.6667px;">[|Mathematical consideration of radioactive decay graph] from www.schoolphysics.co.uk

Define t = T 1/2 , N = N o / 2 and N = N o e <span style="font-family: Symbol,sans-serif; font-size: 9.1px; vertical-align: super;">-l <span style="font-family: Arial,Helvetica,sans-serif; font-size: 9.1px; vertical-align: super;">t \ N = N o / 2 = N o e <span style="font-family: Symbol,sans-serif; font-size: 9.1px; vertical-align: super;">-l T1/2 Take log on each side of equation ln(1/2) = ln e <span style="font-family: Symbol,sans-serif; font-size: 9.1px; vertical-align: super;">-l T1/2 ln(1/2) = <span style="font-family: Symbol,sans-serif;">-l T <span style="font-family: Symbol,sans-serif; font-size: 70%;">1/2 = ln 1 - ln 2 = 0 - ln 2 T 1/2 = ln 2/ l
 * Derivation: T = ln 2 /// l //**

[|Higgs-boson puzzles.pdf] and [|the answers]

**Blackbody** Power emitted by an object is proportional to the surface area and the fourth power of the temperature. As substances are heated they start to glow. The hotter the objects are, the more they glow. All objects emit radiation and they will cool to their surroundings, unless they gain energy from other energy sources, leading to thermal equilibrium. It is a perfect emitter and absorber of radiation. No reflection from blackbody. media type=custom key=29107505 [|Blackbody spectrum] from PHET simulation

Entropy always increases as heat transfers from hotter to colder object. It appreas how heat dissipates/spreads out. It is irreversaible process in any isolated system. Entropy of the entire universe has to increase towards the maxium. Entropy is a measure of disorder of things - Boltzman.

S = k log W [|Entrophy of phase changes] from everyscience.com

media type=custom key=29418935 [|A Brief History Of Quantum Mechanics] [|Best 0f Science] ublished on 24 Dec 2009 media type=custom key=29418923 [|Particles and waves: The central mystery of quantum mechanics - Chad Orzel] <span style="background-image: url(">[|TED-Ed] Published on 15 Sep 2014 media type=custom key=29418931 [|Max Planck ~ Quantum Physics] <span style="background-image: url(">[|Dap Dapple] Published on 28 Apr 2013