Suppose you had a detection device that could count every decay event from a radioactive sample of plutonium-239.052156 (t1/2 is 24,000 yr). How many counts per second would you obtain from a sample containing 0.126 g of plutonium-239? (The mass of Pu-239 is 239.052156 u. Assume 1 yr = 365 d

To calculate the number of counts per second obtained from a sample of plutonium-239, you need to consider the decay constant and the number of atoms in the sample.

To start, we'll need to find the number of atoms in the sample. We can calculate this using Avogadro’s number and the molar mass of plutonium-239.

Step 1: Find the number of moles of plutonium-239:
Using the molar mass of plutonium-239 (239.052156 g/mol), divide the mass of the sample (0.126 g) by the molar mass to get the number of moles:
0.126 g / 239.052156 g/mol = 0.00052758 mol

Step 2: Find the number of atoms of plutonium-239:
Multiply the number of moles by Avogadro's number (6.022 x 10^23 atoms/mol) to find the number of atoms in the sample:
0.00052758 mol x (6.022 x 10^23 atoms/mol) = 3.175 x 10^20 atoms

Now that we have the number of atoms in the sample, we can calculate the number of decay events per second. The decay constant (λ) is related to the half-life (t1/2) by the equation:

λ = ln(2) / t1/2

where ln(2) is the natural logarithm of 2.

Step 3: Calculate the decay constant:
Using the given half-life (24,000 years) and the conversion factor for years to seconds (1 year = 365 days = 24 hours = 3600 seconds), we can calculate the decay constant:
λ = ln(2) / (24,000 years x 365 days/year x 24 hours/day x 3600 seconds/hour)
λ ≈ 4.955 x 10^-15 s^-1

Step 4: Calculate the number of counts per second:
Multiply the number of atoms in the sample by the decay constant to find the number of decay events per second:
Number of counts per second = (3.175 x 10^20 atoms) x (4.955 x 10^-15 s^-1) ≈ 1.574 x 10^6 counts/s

Therefore, you would obtain approximately 1.574 x 10^6 counts per second from a sample containing 0.126 g of plutonium-239.