|\^/| Maple 9 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2003 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > # ************************************************************* > restart; # alles zurücksetzen > with(student); # Standardpakete laden [D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, completesquare, distance, equate, integrand, intercept, intparts, leftbox, leftsum, makeproc, middlebox, middlesum, midpoint, powsubs, rightbox, rightsum, showtangent, simpson, slope, summand, trapezoid] > # ************************************************************* > > # Elementabhängig > # Anzahl Nukleonen > n := 143; # Nd n := 143 > #n := 45; # Ca > > z := 1; # Ladung des Teilchen z := 1 > > # Geräte abhängige Variablen > U := 6000; # Beschleunigungsspannung U := 6000 > r := 0.5; # Radius (Mitte des Kollektorbereichs) r := 0.5 > l := 0.6; # Länge vom Magneten bis zum Kollektor l := 0.6 > > # Allgemeine Variablen > e := 1.602e-19; -18 e := 0.1602 10 > m := 1.674e-27; -26 m := 0.1674 10 > > # ************************************************************* > # Formeln > v := sqrt((2*z*e*U)/(n*m)); v := 89614.05581 > eq1 := r=(n*m*v)/(z*e*B); 0.1339075650 eq1 := 0.5 = ------------ B > > # lösen nach B > r_c := r; r_c := 0.5 > B := solve(eq1,B); B := 0.2678151300 > > # Rückwärts auflösen > # Alle Variablen die gesucht werden löschen > unassign('r'); > unassign('d'); > unassign('n'); > > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > eq2 := d = r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) eq2 := d = r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > > d_abweichung := 30/1000; d_abweichung := 3/100 > d := d_abweichung; d := 3/100 > r_plus := solve(eq2,r); r_plus := 0.5269146073, 1.924563811 > d := -d_abweichung; -3 d := --- 100 > r_minus := solve(eq2,r); r_minus := 0.4766501768, 2.089379488 > > # Jeweils den Wert nehmen, der Näher bei r_c ist. > eq3 := r_h = min(r_list[1]-0.5, r_list[2]-r_c)+r_c; eq3 := r_h = min(r_list[1] - 0.5, r_list[2] - 0.5) + 0.5 > > r_list := r_plus; r_list := 0.5269146073, 1.924563811 > r_max := solve(eq3,r_h); r_max := 0.5269146073 > > r_list := r_minus; r_list := 0.4766501768, 2.089379488 > r_min := solve(eq3,r_h); r_min := 0.4766501768 > > eq1 := r=(n*m*v)/(z*e*B); eq1 := r = 0.003496503495 n > > r := r_min; r := 0.4766501768 > n_min := solve(eq1,n); n_min := 136.3219506 > > r := r_max; r := 0.5269146073 > n_max := solve(eq1,n); n_max := 150.6975778 > > # Minimal und maximal Messbare Elemente in AMU > n_min; n_max; 136.3219506 150.6975778 > > # ************************************************************* > # Isotope von Nd berechnen > # Neues r berechnen für n := 142, 143, 144, 145, 146, 148, 150; > unassign('r'); > n := 142; n := 142 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.4965034963 > d142 := d; d142 := -0.004237768941 > > unassign('r'); > n := 143; n := 143 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.4999999998 > d143 := d; -9 d143 := -0.2400000001 10 > > unassign('r'); > n := 144; n := 144 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.5034965033 > d144 := d; d144 := 0.004154626105 > > unassign('r'); > n := 145; n := 145 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.5069930068 > d145 := d; d145 := 0.008228419292 > > unassign('r'); > n := 146; n := 146 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.5104895103 > d146 := d; d146 := 0.01222359014 > > unassign('r'); > n := 148; n := 148 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); r := 0.5174825173 > d148 := d; d148 := 0.01998645055 > > unassign('r'); > n := 150; n := 150 > alpha := arcsin((r-r_c)/r); r - 0.5 alpha := arcsin(-------) r > d := r*cos(alpha)-r+l*tan(alpha); / 2\1/2 | (r - 0.5) | 0.6 (r - 0.5) d := r |1 - ----------| - r + --------------------- | 2 | / 2\1/2 \ r / | (r - 0.5) | r |1 - ----------| | 2 | \ r / > r := solve(eq1,r); bytes used=4000032, alloc=3276200, time=0.14 r := 0.5244755242 > d150 := d; d150 := 0.02745913169 > > # Ausgabe der Werte > # Abweichung von der Mitte [mm] > d142*1000; d143*1000; d144*1000; d145*1000; d146*1000; d148*1000; d150*1000; -4.237768941 -6 -0.2400000001 10 4.154626105 8.228419292 12.22359014 19.98645055 27.45913169 > # Benötigter Abstand [mm] > (d150-d142)*1000; 31.69690063 >