Calculate the different in energy (AE) between the n=4 and n-5 states for a partcle c mass 6.3 x 10 kg trapped within in a one-dimension well of length 3.0 A. Give your answer in unit ev.
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- Identify the initial and final states if an electron in hydrogen emits a photon with a wavelength of 656 nm. Enter your answers numerically separated by a comma.475 cm /volt-s, and E, = 1.1 eV, 6? Given these data for Si: 4, = 1350 cm/volt-s, H calculate the following. a) The lifetimes for the electron and for the hole. b) The intrinsic conductivity a at room temperature. c) The temperature dependence of o, assuming that electron collision is dominated by phonon scattering, and plot log o versus 1/T. %3D 7. Repeat Problem 6 for Ge, using Tables 6 L and 6 ?At what temperature would we find about half as many hydrogen atoms in first excited state as in the groundstate?..
- C. For a particle of mass 9.10938356×10-31 kg scooting back and forth on a wire of length 13×10-10 m, compute it's energy in the n = 9 state. Use: π = 3.14159265359 and h = 1.0545718×10-34 Js. Eg J. D. What is the rule for the number of nodes for a particle-in-a-box state as a function of its quantum number? Number of nodes = On ΟΙ O n-1 On--1Starting from the N(p) expression of a 3D conductor, derive an expression for the exact density of states D(E) for the 3D conductor in the below graph (You have to show all the steps that lead to your final answer). The length of the conductor is given as L = 20 nm and the diameter is given as D= 4 nm. The +E.. 2mo energy momentum relationship is given as: E =Consider a three-dimensional infinite potential well with a quantized energy of Enn,n, %3D (n + ng + n). where n = 1,2,3, ..,n, = 1,2,3, .., n, = 1,2,3, and a represents the 2ma potential well width in the x, y, and z directions. i. The lowest energy level that the electron may occupy is ii. The values of (ng, ny, ng) for the next higher energy level that is above the lowest energy level can be iii. If the electron drops from the energy level in item (ii) to the energy level in item (i), what is the wavelength of a photon that may be emitted if the work function is 0.4 V? Assume a=0.1 iv. Let the wave function has the general form Y(x,y, z) Asin nyy sin sin The value of A would be, v. Let (n, = 2, n, = 2,n, = 2). What is the probability that an electron exists in the intervals Osxs 0sys and o s z s?
- A spin-1/2 particle is in some initial state with S, = h/2 %3D where în = sin(@)î + cos(0)k in a constant magnetic field Bo oriented along the +z direction. H = @0S2 Calculate AE and At using the energy-time uncertainty relation.Given that the width of an energy band is 10 eV, calculate the following, in cm and eV unit. Consider temperature as 420 K. I) The density of states at 8 kT above the bottom of the band. II) The number of states per unit volume within an energy -3 range of 8 kT to 46 kT from the bottom of the band. Note that this is NOT a small energy range.The excited electronic coufiguration (1s)'(2s)' of the heliun aton can exist as either a singlet or a triplet st.ate. Tell which state has the lower energy and explain why. Give an expression which represents the energy separation between the singlet and triplet states in terms of the one-electron orbitals v1.(r) and 2,(r).
- I1 This time, let us consider a maxed spin state in which the electrons have equal probabilities of being in the pure states 8x+) and sy+)..1. Derive the density of states as a function of energy for a purely two-dimensional electron system. Show the result in a graph and compare qualitatively with that for 0, 1 and 3 dimensions (1 page maximum).Write down the confi gurations for the ground states of calcium and aluminum. What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom