normalise the ground state of the quantum harmonic oscillator that you found in by calculating the value of c, for an alpha particle with a mass of 6.645 * 10 ^-27 kg and frequency of3.17 * 10^-8 hz u(x) = Ce ^-(mwx^2/2h)
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- One of the bound states of positronium has a lifetime given in natural units by T = 2/mas where m is the mass of the electron and a is the fine structure con- stant. Using dimensional arguments introduce the factors ħ and c and determine T in seconds.If the energy levels of an oscillator are given by z,nhv, where n= 0, 1 and 2. Assuming that B= 1/hv, the probability of the oscillator to occupy the third energy level is: A. 13% В. 19% с. 31% D. 51% E. 91% A C D EConsider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 250C.a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz, calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n).
- What is the energy of H2 trapped in a zeolite, which can be modeled by a particle in a cube given nX = 10, nY = 10, nZ = 10 and LX = LY = LZ = 10−9 m.= = Imagine that we have a box that emits electrons in a definite but unknown spin state y). If we send electrons from this box through an SGz device, we find that 20% are determined to have Sz +ħ and 80% to have S₂ -ħ. If we send electrons from this box through an SGx device, we find that 90% are determined to have Sx +ħ and 10% to have Sx Determine the state vector for electrons emerging from the box. You may assume that the vector components are real. -1/ħ. = -Find the relation between spontaneous emission lifetime and cross section for a simple atomic transition.
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- Assume that an atomic nucleus can be thought of as a three-dimensional box with a width of 2 x 10^-14 m. If a proton moving as particles in this box, specify : The energy of the base state of the proton in MeVThe wavefunction of an hydrogenic atom in its ground state is: 1 Z 3/2 Zr Φο a0 ao where Z is the atomic number and do the bohr radius. 1) Give an expression of a。 as a function of the reduced mass. What is the reduced mass of a tritium atom (you can assume that the mass of a neutron to be the same as the mass of a proton)? What is the reduced mass of ³He+? How do they compare to the mass of an electron? 2) What is the wavefunction of a tritium atom in its ground state? What is the wavefunction of ³He+ in its ground state?Suppose that the uncertainty in position of an electron is equal to the radius of the n=1n=1 Bohr orbit, about 0.529×10−10m0.529×10−10m. A) Calculate the minimum uncertainty in the corresponding momentum component. Express your answer in kilogram meters per second. B) Compare this with the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. Compare this with the magnitude of the momentum of the electron in the Bohr orbit. a) This is greater than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. b) This is the same as the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit. c) This is less than the magnitude of the momentum of the electron in the n=1n=1 Bohr orbit.