Question

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

Answer 1

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)