Consider a system having three energy levels with energies 0, 2ɛ and 3ɛ ,with respective degeneracies of 2,2 and 3. Four bosons of spin zero have to be accommodated in these levels such that the total energy of the system is 10 ɛ . The number of ways in which it can be done is
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- This is the graph of function h. 2 T -2 Y 1 2 3 4 →x What is the graph of its derivative, h'?Consider the formation of the resonance A (1,236) due to the incidence of лand л¯ оn р. Assuming that at the resonance energy the I = 1/2 contri- bution to the л+ p interaction is negligible show that at the resonance peak o(r+ + p→ A) o(л+р→ A) = 3Use Dirac notation to calculate the separations in energy levels for a spin system consisting of two protons.
- Calculate the height of the potential barrier for a head on collision of two deuterons.Suppose you are given 3 distinguisable Particles that can be placed in a two Stales with energy different energy 23= (2₁)³², where Show that Zis Sin single particle partition function Clearly white all posible configuration while writing the pactition function. .عره Screenshot has been saved to/Pictures/ScreenshotHence show that (u/beta)
- In Rutherford scattering we noted that angular momentum is conserved. The angular momentum of the incident αparticle relative to the target nucleus is mv0b where m is the mass, v0 is the initial velocity of the αparticle, and b is the impact parameter. Start with L = r x p and show that angular momentum is conserved, and the magnitude is given by mv0b along the entire path of theα particle while it is scattered by the Coulomb force from a gold nucleus.Obtain an approximate value for the interaction length (in cm) of a fast proton in lead from the following data: ro = 1.3 x 10-13 cm, Atomic weight of lead = 207, Density of lead = 11.3 g cm³, Avogadro's number = 6x 10²3 molecules mole-1 [University of Durham 1962]The ground state of 17Ne is unstable. Its half-life has been measured to be 109 ms. (a) What is the energy width of the state? (b) List two possible decay mechanisms.
- let Intim> represeat an energy elgen-state f hydragen atom. CaleulateShow that the pairing effect cannot hold for a free photon without the presence of an atomic nucleus. Help: try to solve the relativistic equations of conservation of momentum and energy assuming that if the interaction occursThe spin-orbit interaction is crucial to explain the right building that accommodate protons and neutrons called the shell model, and can be represented by L·S, where L is the orbital angular momentum and S is the spin or intrinsic angular momentum. To understand how the spin-orbit interaction does the trick you'll need to use commutator algebra and deduce whether the spin-orbit interaction L·S commute with the following operators: J?, Jz, L?, Lz and Sz For doing this, you'll need the following relations: J = L+ S. := - L² - s°) L·S = LXSX + LySy + L2SZ