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
activity=dN/dt=3.4E-6*3grams/239 *avagradros number.
To find the activity of the Np-239 sample, we need to use the decay constant and the mass of the sample.
Activity is the rate at which radioactive decay occurs and is expressed in terms of disintegrations per unit time. It is usually measured in Curie (Ci).
The relationship between activity (A), decay constant (λ), and mass (m) of the sample is given by the formula:
A = λ * N * M
Where:
A = Activity
λ = Decay constant
N = Avogadro's number (6.022 × 10^23 atoms/mole)
M = Mass of the sample
First, we need to convert the mass of the sample from milligrams (mg) to grams (g):
3.0 mg = 3.0 × 10^-3 g
Next, we can calculate the number of moles (N):
Number of moles = Mass / Molar mass
The molar mass of Neptunium-239 (Np-239) is 239 g/mol.
Number of moles = (3.0 × 10^-3 g) / (239 g/mol)
Number of moles ≈ 1.255 × 10^-5 mol
Now, we can substitute the values into the activity formula:
A = (3.40 × 10^-6 s^-1) * (6.022 × 10^23 atoms/mol) * (1.255 × 10^-5 mol)
Calculating this gives us the activity of the Np-239 sample in disintegrations per unit time (s^-1). To convert this to Curie (Ci), we need to use the conversion factor:
1 Ci = 3.7 × 10^10 disintegrations/s
So, the final step is to convert the activity from s^-1 to Ci:
Activity (Ci) = Activity (s^-1) / (3.7 × 10^10 disintegrations/s)
Now, you can follow these steps to calculate the activity of the Np-239 sample.