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If the minimum angle between the total angular momentum vector and the z axis is 32.3° (in a singleelectron atom), what is the total angular momentum quantum number?

An electron is in a three-dimensional box. The x- and z-sides of the box have the same length, but the y-side has a different length. The two lowest energy levels are 2.24 eV and 3.47 eV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two. (a) What are the nX, nY, and nZ quantum numbers for each of these two levels? (b) What are the lengths LX, LY, and LZ for each side of the box? (c) What are the energy, the quantum numbers, and the degeneracy (including the spin degeneracy) for the next higher energy state?

Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (?),(n), the angular momentum quantum number (?),(?), the magnetic quantum number (??),(m?), and the spin quantum number (?s)(ms) have strict rules which govern the possible values. Identify all allowable combinations of quantum numbers for an electron. A. ?=4,n=4, ?=1,?=1, ??=2,m?=2, ?s=−1/2ms B.?=3,n=3, ?=−1,?=−1, ??=1,m?=1, ?s=−1/2ms C.?=5,n=5, ?=2,?=2, ??=2,m?=2, ?s=+1/2ms D.?=3,n=3, ?=3,?=3, ??=1,m?=1, ?s=−1/2ms E.?=2,n=2, ?=1,?=1, ??=1,m?=1, ?s=0ms F. ?=3,n=3, ?=1,?=1, ??=1,m?=1, ?s=+1/2