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  1. C

    Energy Level Separation

    Homework Statement Considering only orbital angular momentum, estimate the energy level separation between electron states in a magnetic field of 1 Tesla applied along the z direction. Homework Equations I am confused by how to even start this question! Isn't orbital angular momentum...
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    Eigenvalues and Normalised Eigenvectors

    Homework Statement I have a matrix H= [h g g h] and I need to find the eigenvalues and normalised eigenvectors Homework Equations The Attempt at a Solution I subtracted lamda from the diagonal and then solved for the determinant equally zero. The eigenvalues I found were...
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    Wavefunctions for Indistinguishable and Distinguishable particles -

    Wavefunctions for Indistinguishable and Distinguishable particles - URGENT Homework Statement A one-dimensional potential well has a set of single-particle energy eigenstates Un(x) with energies En=E_o n^2 where n=1,2,3... Two particles are placed in the well with three possible sets of...
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    Energy levels of helium atom

    Homework Statement I have having difficulty explaining the splitting of helium atom energy levels for three different cases: 1)Coulomb interaction is ignored 2)Coulomb interaction is present but exchange interaction is neglected 3)Coulomb and exchange interactions are present The Attempt...
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    Structure factors

    Homework Statement I have the ionic compound cesium chloride and have been asked to use the equation p(k) = (sum over j) exp(-iK.r)f(k) to find the structure factor for x-ray diffraction from cesium and explain why it can take two values. It also asks how you would expect the intensities...
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    Eigenvectors of the hamiltonian

    Homework Statement The Hamiltonian of a system has the matrix representation H=Vo*(1-e , 0 , 0 0 , 1 , e 0 , e , 2) Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e=0) Homework Equations when unperturbed the Hamiltonian will...
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    Exchange interaction

    Homework Statement I was trying to work through some quantum physics questions and I was getting a bit confused. I know that for fermions the wavefunction must consist of spin and spatial parts of the fermionic wavefunction with opposite exchange symmetry (ie antisymmetric spin and symmetric...
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    Energy shift using perturbation theory

    Homework Statement I am looking at the relativistic correction to the kinetic energy for a hydrogen atom. I am told that the perturbation is usually written as H = -p^4/(8 m^3 c^2) and need to find the energy shift Homework Equations I know that from the perturbation theory the energy...
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    Double Pendulum !

    Double Pendulum URGENT! Homework Statement I am trying to solve this past paper question for my exam tomorrow: A double pendulum is constructed using a light rod and light inextensible strings. Two string pendulums hanging from ceiling 1m long. 0.1m from top they are connected by a light...
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    Past paper question about rates

    Homework Statement Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state? Homework Equations Well if the rate of water...
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    Current homework problem

    Homework Statement A light bulb has a straight metal wire filament of 50 micro metres diameter and 10mm long and when powered with a 5V constant voltage supply it draws 0.5A of current. What happens to the current if the filament is replaced with one of three times the diameter? Homework...
  12. C

    Bullet hitting a suspended mass

    Homework Statement A mass of M=0.5kg is suspended from a fixed pivot by a thin rope of length l=120cm. The mass is struck by a bullet of mass m=10g with a speed of v=150m/s which embeds itself into the lead mass. What angle does the combined mass swing back to? The Attempt at a Solution...
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    Hydrogen gas

    Homework Statement A gas of hydrogen atoms has a fraction of atoms found in the n=2 quantum state of 0.05. What is the temperature of the gas? The Attempt at a Solution I think the gas molecules have an energy E=5/2kT (rather than E=kT ?? because diatomic gases have 5 degrees of...
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    Pressure and tyres

    Homework Statement Just a quick question: does a fully inflated tyre have the same mass as a tyre that is punctured or uninflated? Homework Equations The Attempt at a Solution The one that is fully inflated will have a greater pressure but I am not sure what this will mean in...
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    Inclined pendulum

    Homework Statement A train is travelling at 30m/s and decelerates and stops. During this process a passenger notices that a penduum is inclined by 10 degrees to the vertical. Estimate how far the train travels before coming to rest Homework Equations The Attempt at a Solution I...
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    Angular resolution of the eye

    Homework Statement Two red lights are separated by 5cm, perpendicular to your line of sight. How far away from them are you if they can just be resolved with the naked eye? Homework Equations angular resolution =sin(theta)=1.22lambda / D spatial resolution = 1.22(focal length * lambda)/D...
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    Newton's law of cooling and your body

    Homework Statement a body has temperature 27C at twelve oclock. The room temperature is constant at 16C. Two hours later the body was found to have a temperature of 24C. The temperature of a normal human body is 37C.Using Newton's law of cooling estimate the time of death. Homework...
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    Orthogonality and find coefficients

    Homework Statement I have that the general solution of a function is f(\rho,t)=\Sigmac(m)Jo(\alpha\rho\a) exp[-Dtm^2] where c(m) are constants. I need to find an expression for c(m) in terms of an integral Homework Equations Orthogonality relation given is \intdx x...
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    Fast help please: solving differential equations

    Homework Statement I have the equation -(ck^2)U(k,t)=d^2/dt U(k,t). And I need to find the general solution. Homework Equations The Attempt at a Solution I can rearrange this into the form d^2 U/dt^2 + (ck^2)U(k,t)=0 but I am not sure of the form of the solution to this equation...
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    Integrating the delta function

    Homework Statement By using the substitution u=cosx obtain the value of the integral \int\delta(cosx-1/2)dx between 0 and pi Homework Equations I have no idea how to go any further with this apart from substituting in for u!? The Attempt at a Solution
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    Fourier transform of hat function

    Homework Statement obtaining the fourier transform of the hat function h(x) = 1 if modulus of x</= 1 =0 otherwise Homework Equations F(k)=1/sqrt(2*PI) *integral from -1 to 1 of exp(ikx) The Attempt at a Solution I've carried through the transform and got an answer of...
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    Braggs reflections

    Homework Statement How would you expect the intensities of the Bragg reflections in the x-ray diffraction patterns of cesium, cesium chloride and cesium iodide to compare? (The atomic numbers of cesium, chlorine and iodine are 55, 17 and 53 respectively_ Homework Equations The...
  23. C

    Structure factor

    Homework Statement Sodium chloride has a face-centred cubic structure which can be regarded as a primitive cubic structure with a basis of sodium atoms at fractional coordinatese (0,0,0) (0.5,0.5,0) (0,0.5,0.5) and (0.5,0,0.5) and chlorine atoms at (0.5,0,0) (0,0.5,0) (0,0,0.5) and...
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    4-vectors scalar product

    Homework Statement If a and b are 4-vectors give the definition of the scalar product a.b and demonstrate its Lorentz invariance Homework Equations The Attempt at a Solution So (with 4-vectors double underlined!) a.b = a0b0-a1b1-a2b2-a3b3 a' = (a0*gamma - beta*gamma a1 ...
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    4 vectors

    Homework Statement I am aving a bit of trouble understanding how to show something is a 4 vector. For example K = (v/c, 1/lamdba, 0, 0 ) Show it is a 4-vector. I am not quite sure how to start this. Similarly I have the amplitude of a wave in frame S described as A=cos[2PI(vt-x/lambda)] and...
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    Minimising helmholtz free energy

    Homework Statement Show that the most probable energy minimises the Helmholtz free energy. Homework Equations F=E-TS(E) where S(E) is the entropy of te system of given energy E. The Attempt at a Solution Not sure how you would 'show' is ???? P(E) = 1/Z *weight funciton*exp(-beta E)
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    Components of Earth's angular velocity vector

    Homework Statement Using a coordinate system in whic x and y are due east and nort of the city and z is the radial distance outwards from te centre of te earth, find the compnents of w the earth's angular velocity vector. You may assume that the latitude of the city is lamdba = 34degrees...
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    Degenerate states of 2 particles in a 1D harmonic oscillator potential

    Homework Statement "Two non-interacting particles are placed in a one-dimensional harmonic oscillator potential. What are the degeneracies of the two lowest energy states of the system if the particles are a)identical spinless bosons b)identical spin-1/2 fermions? Homework Equations...
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    Charge distribution over two thin concentric spherical shells

    Homework Statement "A thin conducting spherical shell of radius a carries a charge q. Concentric with this is another spherical shell of radius b>a carrying a net charge Q. Describe how the charge is distributed between the inner and outer surfaces of the shells. What is te capacitance of the...
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    Magnetic flux and emf through a rotating ring

    Homework Statement Homework Equations The Attempt at a Solution
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