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 terms of grams per second, we can use the following steps:
Step 1: Convert the activity from curies (Ci) to disintegrations per second (dps):
Given, 1 Ci = 3.700 × 10^10 dps
So, the activity in dps is:
0.0730 Ci * (3.700 × 10^10 dps / 1 Ci) = 2.701 × 10^9 dps
Step 2: Convert the disintegrations per second to the rate of decomposition in moles per second:
Since 139Cs has a molar mass of 138.9134 amu, we'll use the conversion factor:
1 amu = 1.66054 × 10^(-24) g
Since 1 mol of any substance contains Avogadro's number (6.022 × 10^23) of particles, we can calculate the rate of decomposition in moles per second as follows:
Rate (in moles/s) = (dps) / (Avogadro's number)
Rate (in moles/s) = 2.701 × 10^9 dps / (6.022 × 10^23)
Step 3: Convert the rate from moles per second to grams per second:
Since we know the molar mass of 139Cs is 138.9134 amu, we can use the conversion factor:
1 mol = 138.9134 g
Rate (in grams/s) = (Rate in moles/s) * (molar mass in g/mol)
Rate (in grams/s) = (2.701 × 10^9 dps / (6.022 × 10^23)) * (138.9134 g/mol)
Now we can perform the calculations to find the instantaneous rate of decomposition of 139Cs in grams per second.