# HW8 - HY28 N0 8 d 1 a What are the possible values of Pfor...

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Unformatted text preview: HY28 - N0. 8 - d 1. a) What are the possible values of Pfor n=6? b) What are the possible values of m,for 1:6? .c) What is the smallest possible value of n for whichFcan be 4? d) . What is the smallest possible! that can have a 2 component of 4h? 2. An electron is in the n=4, 1:3 state of hydrogen. a) What is the length of the electron's angular momentum vector? b) How many different possible 2 components can the angular momentum vector have? List the possible 2 components. c) Would your answers to a) and b) change if the principle quantum number n were 5 instead of 4? ' 3. Show that the wave function ‘I’mo(r,6,¢) is properly normalized (see Table 7.1 of your book). (*) 4. Show by direct substitution that the wave function corresponding to n=1,I=O, m,=0 is a solution of Equation 7.3 (page 208 in your text book) corresponding to the ground-state energy of hydrogen. 5. Find the values of the radius where the n=2, [:0 radial probability density has its maximum values. 6. The mean or average value of the radius r can be found according to rm: ] rP(r)dr. Show that the mean value of r for the ls state of hydrogen is (3/2)a0. (*) 0 . 09 (*) Use: 3 n -—Clx d n .l X e X = Qua—1 O 75” Q 63 A‘jloo (59%)) = 0‘) \E\=Jﬁ (NH :18? WW 5) WERE IKE ZJZHJr {959M % CM¥W1 Lib wit 2 +gtj+21aj+m O)~t/~th"3t C) Hm 6F Tﬁﬁgf ﬁﬁZULR MW 69/ n L _2\ 47610 WW as“ e 2 00 TP 21y Z W AV = S r? 01k X 9M9 laid) WWW! 0 0 0 - L :L w ' a. W 2T ".4 ‘ [W Q03 Salk/D kgﬂllr =32 Egg/49% 0 D o v 0 “SR/‘6 AX \ EL N 4— ‘ a; (2/6103 “ é [_‘t\1 L \ ~V/a Z ' 2 __ 2 C o a w 610 _ L A” a _ 2m 4k. We 6 mer a] — _ :rﬁ L _ 2 2 x _ _J_e__ _ 2m L 0‘02 We) LIrmr — E iqy ﬂ 1 MA J2 H + c; @621. £5“ E 2H4 “111120 t k _‘ "my / E ﬂ H W143 32‘ t2 “rial wag [imam Ei mam EQUAle 3E; '2. 2 2 Cr : Y L t r 2 R 10 ) WM HI Y Mug (2 f0) 2 r/ao 1+ r: ’ FUR V1“ {:0 6102 2:: Z |/' / / ﬂ PU): L? H Yl— gig “r/aa av QDZ e f %T (if z p dr :9 L gq'x k 0"" r 4‘3 )6 o *(VVZAEI +%)6‘Vao[ 9 n m Jr ~r/a ke 0 \LE EL '2 3 Kat} L aar+qur »§;}— +%L2r2_:‘_i: L”, _____ ._ Mm > D qv’g 2 Q0? J 2‘ k [ﬁg/52 " k, a n [2 «0 THE?) “gag—D) W1 mm k: W hut/rm W ...
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## This note was uploaded on 07/15/2010 for the course MATH 521 taught by Professor Metcalfe during the Spring '10 term at University of North Carolina Wilmington.

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HW8 - HY28 N0 8 d 1 a What are the possible values of Pfor...

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