homework#3 solutions Section 2.4 #2. If S = f1=n¡1=m: n;m 2 Ng, find inf S and supS: Answer. We claim inf S = ¡1: Let 1=n¡1=m be an arbitrary element in S: Then, 1=n¡1=m ‚ 1=n¡1 > ¡1: So ¡1 is a lower bound for S: Let † > 0: By Corollary 2.4.5, there exists n0 2 N such that 1=n0 < †: Now, 1=n0 ¡1 < †¡1 = ¡1+† and 1=n0 ¡1 2 S: Thus, ¡1 = inf S: We claim supS = 1: Note
No two electrons in an atom can have the same set of quantum numbers. The first quantum number is the principle quantum number , which is n=3. This means the electron is in the third energy level shell. The second quantum number, the angular momentum , is l=2, and means the electron is in the "d" sublevel subshell. The third quantum number, the magnetic quantum number , m_l=2, represents one of the five "3d" orbitals. Lastly, we have the spin quantum number , m_s=-1/2. It indicates the direction of the spin of the electron. Each electron in an atom has a unique set of quantum numbers. The given quantum numbers for the electron in the question tell us that there is a high probability that the electron is in one of the "3d" orbitals of the atom. Resources
Sc h o o l Re c o m m e n d a t i o n Gr a d e s K - 1 2 S t u d e n t N a m e