If a sample of the radioactive nuclide 139Cs has an activity of 0.0730 Ci, what is the instantaneous rate of decomposition of 139Cs in terms of grams per second? The mass of 139Cs is 138.9134 amu.
(1 Ci = 3.700 × 1010 disintegrations/s, 1 amu = 1.66054 × 10–24 g)
To find the instantaneous rate of decomposition of 139Cs in grams per second, we need to convert the activity from curies (Ci) to disintegrations per second and then to grams per second.
First, let's convert the activity from curies to disintegrations per second. We know that 1 Ci = 3.700 × 10^10 disintegrations/s.
Activity in disintegrations per second = 0.0730 Ci * 3.700 × 10^10 disintegrations/s
Activity in disintegrations per second = 2.701 × 10^9 disintegrations/s
Next, we need to find the molar mass of 139Cs in grams. We are given that the mass of 139Cs is 138.9134 amu, and we know that 1 amu = 1.66054 × 10–24 g.
Molar mass of 139Cs in grams = 138.9134 amu * 1.66054 × 10–24 g/amu
Molar mass of 139Cs in grams = 2.306 × 10^–22 g
Now, we can calculate the instantaneous rate of decomposition of 139Cs in grams per second. The rate is given by the equation:
Rate (grams per second) = (Activity in disintegrations per second) * (Molar mass of 139Cs in grams)
Rate = (2.701 × 10^9 disintegrations/s) * (2.306 × 10^–22 g)
Rate ≈ 6.230 × 10^–13 grams per second
So, the instantaneous rate of decomposition of 139Cs is approximately 6.230 × 10^–13 grams per second.