A radioactive source of a single nuclide emits 2.4-MeV neutrons at the rate of 9200 neutrons per second. The number of atoms in the source is 4.0 ×109. The activity of the source, in nCi, is
To find the activity of the radioactive source, we can use the formula:
Activity = Decay constant × Number of radioactive atoms
First, we need to find the decay constant, which is given by the equation:
Decay constant = λ = ln(2) / Half-life
The half-life of the nuclide is not given in the question, so we need to find it. However, we are given the energy of the emitted neutrons and the mass of the nuclide, so we can try to deduce the half-life using the equation:
Q = T × (Average energy per decay event)
where Q is the energy released per decay event and T is the half-life.
From the question, we know the energy released per decay event (Q) is 2.4 MeV. We also know that the number of decay events per second is given by the activity of the source. So, we can write:
Q × Activity = Power = (Energy per second) = Mass × (Specific heat capacity) × (Temperature change per second)
From this equation, we can rearrange to solve for the half-life:
T = (Q × Activity) / (Mass × Specific heat capacity × Temperature change per second)
Since we do not have information about the mass, specific heat capacity, or temperature change, we cannot directly determine the half-life. Therefore, we cannot accurately calculate the decay constant, and thus, we are unable to find the activity of the source.