In: Chemistry
1) If a sample of the radioactive nucleide ^139Cs has an activity of 2.93 Ci, what is the instantaneous rate of decomposition of ^139Cs in terms of grams per second? The mass of ^139Cs is 138.9134amu. (1 Ci = 3.700*10^10 disintegrations/s, 1 amu = 1.66054*10^-24 g)
A. 2.93*10^-2 g/s
B. 6.76*10^-24 g/s
C. 8.53*10^-12 g/s
D. 1.83*10^-34 g/s
E. 2.5*10^-11 g/s
2) the half-life of the radioactive nucleide ^79As is 9.0min. what is the activity of a 9.8g sample of ^79As? The molar mass of ^79As is 78.921g/mol. (1 Ci = 3.700*10^10 disintegrations/s)
A. 3.7*10^3 Ci
B. 2.4*10^-15 Ci
C. 2.6*10^9 Ci
D. 1.6*10^5 Ci
E. 2.3*10^-10 Ci
2.93 CI= 2.93*3.7*1010 disintegration/s =10.841*1010 disintegration/s
138.9134 amu of elements correspond to 138.9134*1.66054*10-24 gm =2.31*10-22 gm
Hence gm/s = 10.841*1010* 2.31*10-22 gm/s =2.5*10-11 gm/s ( E is correct)
2. since the decay is 1st order, Rate constant , K= 0.693/ half life= 0.693/ 9 = 0.077/min=0.077/60= 0.0013/sec
A=activity = rate constant* N
N= no of atoms
Moles of elements= mass/Molar mass = 9.8/78.921 =0.1242
mole of any substance contains 6.023*1023 atoms, hence 0.1242 moles contains 0.1242*6.023*1023 atom =7.5*1022atom
Hence activity = 0.0013*7.5*1022 =9.75*1019 disintegration/s
1CI= 3.7*1010 disintegration/s
6*1021 disintegration/s= 9.75 *1019/ (3.7*1010)= 2.6*109 Ci ( C is correct)