CALCULATIONS: Uranium 238 Decay
Case 1
10 REM File name: URANIUM1.BAS,DOC,BAK.
20 REM To calculate U238 decay in 4 nuclei of 140,60,37,1 mass unit, in
30 REM SR and AD through momentum conservation and mass-energy conservation.
40 M1=140
50 M2=60
60 M3=37
70 M4=1
75 MT=238
80 U=931.5
90 REM SR Momentum calculation.
100 B1=8.414001E-03
110 B2=4.000001E-03
120 B3=6.778888E-03
130 B4=.56638
131 PRINT"TO MAKE SR MOMENTUM CONSERVATION"
132 PRINT "B1="B1;"B2="B2;"B3="B3;"B4="B4
140 M1R=M1*U*B1*(1/(SQR(1-B1^2)))
150 M2R=M2*U*B2*(1/(SQR(1-B2^2)))
160 M3R=M3*U*B3*(1/(SQR(1-B3^2)))
170 M4R=M4*U*B4*(1/(SQR(1-B4^2)))
180 PRINT " SR MOMENTUM"
190 PRINT M1R;M2R;M3R;M4R
200 SMR=M2R+M3R+M4R
210 PRINT "SMR ="SMR
220 PRINT " SR KINETIC ENERGY"
230 KE1R=M1*U*((1/(SQR(1-B1^2)))-1)
240 KE2R=M2*U*((1/(SQR(1-B2^2)))-1)
250 KE3R=M3*U*((1/(SQR(1-B3^2)))-1)
260 KE4R=M4*U*((1/(SQR(1-B4^2)))-1)
270 PRINT KE1R;KE2R;KE3R;KE4R
280 KESR=KE1R+KE2R+KE3R+KE4R
290 PRINT "KESR ="KESR "------ SR KE SUM"
300 PRINT" SR MASS INCREMENT"
310 MI1R=M1*(1/(SQR(1-B1^2)))
320 MI2R=M2*(1/(SQR(1-B2^2)))
330 MI3R=M3*(1/(SQR(1-B3^2)))
340 MI4R=M4*(1/(SQR(1-B4^2)))
350 PRINT MI1R;MI2R;MI3R;MI4R " **SR MASS INCREMENT**"
360 MSR=MI1R+MI2R+MI3R+MI4R
370 PRINT "MSR ="MSR
371 DR=MSR-MT
372 DRKE=DR*U
373 PRINT "DRKE ="DRKE "------ SR KE BY MASS INCREMENT"
374 REM AD MOMENTUM CALCULATION
380 M1A=M1*U*B1*SQR(1-B1^2)
390 M2A=M2*U*B2*SQR(1-B2^2)
400 M3A=M3*U*B3*SQR(1-B3^2)
410 M4A=M4*U*B4*SQR(1-B4^2)
420 PRINT
430 PRINT" AD MOMENRUM"
440 PRINT M1A;M2A;M3A;M4A
450 SMA=M2A+M3A+M4A
460 PRINT "SMA ="SMA
470 PRINT" AD KINETIC ENERGY"
480 KE1A=M1*U*(1-SQR(1-B1^2))
490 KE2A=M2*U*(1-SQR(1-B2^2))
500 KE3A=M3*U*(1-SQR(1-B3^2))
510 KE4A=M4*U*(1-SQR(1-B4^2))
520 PRINT KE1A;KE2A;KE3A;KE4A
530 KESA=KE1A+KE2A+KE3A+KE4A
540 PRINT "KESA ="KESA " ===== AD KE SUM"
550 PRINT" AD MASS DECREMENT"
560 MD1A=M1*SQR(1-B1^2)
570 MD2A=M2*SQR(1-B2^2)
580 MD3A=M3*SQR(1-B3^2)
590 MD4A=M4*SQR(1-B4^2)
600 PRINT MD1A;MD2A;MD3A;MD4A " **AD MASS DECREMENT**"
610 SMDA=MD1A+MD2A+MD3A+MD4A
620 PRINT "SMDA ="SMDA
630 DA=MT-SMDA
640 DAKE=DA*U
650 PRINT "DAKE ="DAKE " ===== AD KE by MASS DECREMENT"
Program Output
B1= 8.414001E-03 B2= 4.000001E-03 B3= 6.778888E-03 B4= .56638
SR MOMENTUM
1097.309 223.5619 233.6431 640.1586
SMR = 1097.364
SR KINETIC ENERGY
4.617187 .4463947 .7929613 198.7633
KESR = 204.6199 ------ SR KE SUM
SR MASS INCREMENT
140.005 60.00048 37.00085 1.12338 **SR MASS INCREMENT**
MSR = 238.2197
DRKE = 204.6184 ------ SR KE BY MASS INCREMENT
AD MOMENTUM
1097.231 223.5583 233.6324 640.8045
SMA = 891.9951
AD KINETIC ENERGY
4.617187 .4463947 .7929613 163.8097
KESA = 169.6662 ====== AD KE SUM
AD MASS INCREMENT
139.995 59.99952 36.99915 .8241442 **AD MASS INCREMENT**
SMDA = 237.8179
DAKE = 169.6673 ====== AD KE by MASS INCREMENT
Case 2
10 REM File name: URANIUM2.BAS,DOC,BAK.
20 REM To calculate U238 decay in 4 nuclei of 140,60,37,1 mass unit, in
30 REM SR and AD through momentum conservation and mass-energy conservation.
40 M1=140
50 M2=60
60 M3=37
70 M4=1
75 MT=238
80 U=931.5
90 REM SR Momentum calculation.
100 B1=7.600001E-03
110 B2=5.772801E-03
120 B3=6.778888E-03
130 B4=.56638
131 PRINT"TO MAKE AD MOMENTUM CONSERVATION"
132 PRINT "B1="B1;"B2="B2;"B3="B3;"B4="B4
140 M1R=M1*U*B1*(1/(SQR(1-B1^2)))
150 M2R=M2*U*B2*(1/(SQR(1-B2^2)))
160 M3R=M3*U*B3*(1/(SQR(1-B3^2)))
170 M4R=M4*U*B4*(1/(SQR(1-B4^2)))
180 PRINT " SR MOMENTUM"
190 PRINT M1R;M2R;M3R;M4R
200 SMR=M2R+M3R+M4R
210 PRINT "SMR ="SMR
220 PRINT " SR KINETIC ENERGY"
230 KE1R=M1*U*((1/(SQR(1-B1^2)))-1)
240 KE2R=M2*U*((1/(SQR(1-B2^2)))-1)
250 KE3R=M3*U*((1/(SQR(1-B3^2)))-1)
260 KE4R=M4*U*((1/(SQR(1-B4^2)))-1)
270 PRINT KE1R;KE2R;KE3R;KE4R
280 KESR=KE1R+KE2R+KE3R+KE4R
290 PRINT "KESR ="KESR "------ SR KE SUM"
300 PRINT" SR MASS INCREMENT"
310 MI1R=M1*(1/(SQR(1-B1^2)))
320 MI2R=M2*(1/(SQR(1-B2^2)))
330 MI3R=M3*(1/(SQR(1-B3^2)))
340 MI4R=M4*(1/(SQR(1-B4^2)))
350 PRINT MI1R;MI2R;MI3R;MI4R " **SR MASS INCREMENT**"
360 MSR=MI1R+MI2R+MI3R+MI4R
370 PRINT "MSR ="MSR
371 DR=MSR-MT
372 DRKE=DR*U
373 PRINT "DRKE ="DRKE "------ SR KE BY MASS INCREMENT"
374 REM AD MOMENTUN CONSERVATION.
380 M1A=M1*U*B1*SQR(1-B1^2)
390 M2A=M2*U*B2*SQR(1-B2^2)
400 M3A=M3*U*B3*SQR(1-B3^2)
410 M4A=M4*U*B4*SQR(1-B4^2)
420 PRINT
430 PRINT" AD MOMENRUM"
440 PRINT M1A;M2A;M3A;M4A
450 SMA=M2A+M3A+M4A
460 PRINT "SMA ="SMA
470 PRINT" AD KINETIC ENERGY"
480 KE1A=M1*U*(1-SQR(1-B1^2))
490 KE2A=M2*U*(1-SQR(1-B2^2))
500 KE3A=M3*U*(1-SQR(1-B3^2))
510 KE4A=M4*U*(1-SQR(1-B4^2))
520 PRINT KE1A;KE2A;KE3A;KE4A
530 KESA=KE1A+KE2A+KE3A+KE4A
540 PRINT "KESA ="KESA " ===== AD KE SUM"
550 PRINT" AD MASS DECREMENT"
560 MD1A=M1*SQR(1-B1^2)
570 MD2A=M2*SQR(1-B2^2)
580 MD3A=M3*SQR(1-B3^2)
590 MD4A=M4*SQR(1-B4^2)
600 PRINT MD1A;MD2A;MD3A;MD4A " **AD MASS DECREMENT**"
610 SMDA=MD1A+MD2A+MD3A+MD4A
620 PRINT "SMDA ="SMDA
630 DA=MT-SMDA
640 DAKE=DA*U
650 PRINT "DAKE ="DAKE " ===== AD KE by MASS DECREMENT"
Program Output
B1= 7.600001E-03 B2= 5.772801E-03 B3= 6.778888E-03 B4= .56638
SR MOMENTUM
991.1448 322.6472 233.6431 640.1586
SMR = 1097.364
SR KINETIC ENERGY
3.777698 .932765 .7929613 198.7633
KESR = 204.6199 ------ SR KE SUM
SR MASS INCREMENT
140.0041 60.001 37.00085 1.12338 **SR MASS INCREMENT**
MSR = 238.2198
DRKE = 204.2773 ------ SR KE BY MASS INCREMENT
AD MOMENTUM
991.0875 322,6365 233.6324 640.8045
SMA = 991.0734
AD KINETIC ENERGY
3.769925 .932765 .7929613 163.8097
KESA = 169.6662 ====== AD KE SUM
AD MASS INCREMENT
139.996 59.999 36.99915 .8241442 **AD MASS INCREMENT**
SMDA = 237.8183
DAKE = 169.2977 ====== AD KE by MASS INCREMENT