Consider the seventh excited level of the hydrogen atom. What is the largest angle between the orbital angular momentum and the zz-axis? Express your answer in degrees to three significant figures
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- A) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. D) Determine the value of the total angular momentum L for the H-atom in the orbit l=3 and plot a diagram to show its projections on the z-axis.Calculate the standard uncertainty in z if z=Xsinθ using the angle (45.00 ± 0.74) degrees and the value X = (23.60 ± 0.51) z = ___±___13.10 If the radial momentum p, and radial velocity a, for an electron in a central potential are defined by r.p-ih a.r Pr = Xr= " r r show that ihk Ba, (ap) = ar Pr + r B(o'. L + h) where k = ħ
- Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit. Each electron has orbital angular momentum U (that is, the orbit is the smallest-radius Bohr orbit), and the two electrons are always on opposite sides of the nucleus. Ignore the effects of spin. What is the total kinetic energy of the electrons?Consider the seventh excited level of the hydrogen atom. (a) What is the energy of this level? (b) What is the largest magnitude of the orbital angular momentum? (c) What is the largest angle between the orbital angular momentum and the z-axis?Use the Saha equation to determine the fraction of Hydrogen atoms that are ionized Nu/Ntotal at the center of the Sun, where the temperature is 15.7 million K and the electron number density is ne=6.1x1031 /m³. Don't try to compare your result with actual data, as your result will be lower due to not taking the pressure into account. Since most of the neutral H atoms are in the ground state, use Zrdegeneracy3D2 and, since a H ion is just a proton, Zı=1. Also, use XI=13.6 eV.
- Write down for yourself the expression for the radial distribution function of a 2s electron in a hydrogenic atom and determine the radius in Angstroms at which the electron is most likely to be found. Assume the species has an atomic number of 2. (Ans. in Agstroms)I need help with the last 3.An electron is in an angular momentum state with 1 = 3. What is the length of the electron's angular momentum vector?
- 1.5 The time-averaged potential of a neutral hydrogen atom is given by - ar Ф 4 TTE0 ar 1 + 2 r where q is the magnitude of the electronic charge, and al = Bohr radius. Find the distribution of charge (both continuous and discrete) that will give this potential and interpret your result physically. ao/2, ao being theA hydrogen atom ¹H with 200 eV of kinetic energy has a head-on, perfectly elastic collision with a ¹2C atom at rest. Part A Afterward, what is the kinetic energy, in eV, of ¹H? Express your answer in electron volts. KfH = Submit Part B V Kfc = ΑΣΦ Request Answer Afterward, what is the kinetic energy, in eV, of ¹2C? Express your answer in electron volts. ww ΑΣΦ ? ? eV eVFor each of the following transitions in a hydrogen atom free of external fields, determine whether the electron energy increases, decreases, or remains unchanged. Indicate your answers with I, D, or U. (a) The electron moves from n = 2 to n = 4. (b) The electron moves from n = 4 ton= 3. (c) Within 3 level, the electron moves from e the n = 2 to l =-2. (d) Within the n = 4, € = 2 sublevel, the electron moves from = - 1 to me = + 1. me %3D