Neptunium 239
93 Np has a decay constant of 3.40 ×10-6 s-1. A 3.0-mg sample of Np-239 is
prepared. The activity of the Np-239 sample, in Ci, is
Ok, take the last I gave you, and divide by 3.7E10
how do I solve it?
activityinCi=decayconstant*avadgrado's number*molesNp/3.7E10
= 3.4E-6*3/239*6.023E23/3.7E10
To calculate the activity of Neptunium-239 (Np-239) sample, we need to use the radioactive decay equation:
A = λ * N,
where A is the activity, λ is the decay constant, and N is the number of radioactive atoms present in the sample.
Given the decay constant for Np-239 is 3.40 × 10^-6 s^-1, we can now proceed to calculate the activity.
To find the number of radioactive atoms (N), we need to use the Avogadro's number and the molar mass of Np-239.
The molar mass of Np-239 is 239 g/mol.
Step 1: Convert the mass of the sample to moles.
Since we have a 3.0 mg (milligram) sample, we need to convert it to grams by dividing by 1000:
3.0 mg = 3.0 * 10^-3 g
Then, we can convert grams to moles by dividing by the molar mass:
3.0 * 10^-3 g / 239 g/mol = 1.25523012552 * 10^-5 mol
Step 2: Calculate the number of atoms.
To calculate the number of atoms, we multiply the number of moles by Avogadro's number, which is 6.022 × 10^23 atoms/mol:
1.25523012552 * 10^-5 mol * 6.022 × 10^23 atoms/mol = 7.55635443062 * 10^18 atoms
Step 3: Calculate the activity.
Now that we know the number of radioactive atoms (N) and the decay constant (λ), we can calculate the activity (A) using the equation mentioned earlier:
A = λ * N
A = 3.40 × 10^-6 s^-1 * 7.55635443062 * 10^18 atoms
To convert the activity from units of seconds to curies (Ci), we use the conversion factor:
1 Ci = 3.7 * 10^10 disintegrations per second
A (in Ci) = A (in s^-1) / (3.7 × 10^10 disintegrations/s)
Finally, we can calculate the activity in Ci by plugging in the values:
A (in Ci) = (3.40 × 10^-6 s^-1 * 7.55635443062 * 10^18 atoms) / (3.7 × 10^10 disintegrations/s)
A (in Ci) ≈ 6.92 × 10^8 Ci
Therefore, the activity of the Np-239 sample is approximately 6.92 × 10^8 Ci.