Question

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

Answer 1

[AI-generated answer — Explain Bot]

To find the activity of the radioactive source in nanoCuries (nCi), we need to use the following relation:

Activity (A) = λ × N

Where:
A = Activity of the source in Curie (Ci)
λ = Decay constant of the nuclide (per second)
N = Number of radioactive atoms present

First, let's convert the given number of neutrons emitted per second to the decay constant (λ):

Given:
Neutron energy = 2.4 MeV
Number of neutrons emitted per second = 9200

The energy per neutron can be converted to the decay constant (λ) using the equation:

E = m × c^2

Where:
E = Energy of a single neutron (in Joules)
m = Mass of a single neutron (in kg)
c = Speed of light (in m/s)

The mass of a neutron is approximately 1.67 x 10^-27 kg.

Using the conversion factor 1 MeV = 1.602 x 10^-13 Joules, we can calculate the energy (E) of a single neutron:

E = 2.4 MeV × 1.602 x 10^-13 Joules/1 MeV

Next, we can calculate the decay constant (λ) using the equation:

λ = Number of neutrons emitted per second / (Number of atoms × E)

Substituting the given values into the equation:

λ = 9200 neutrons/s / (4.0 × 10^9 atoms × E)

Now, we can find the activity (A) in Curie (Ci) using the equation mentioned earlier:

A = λ × N

Substituting the values of λ and N:

A = λ × N = (9200 neutrons/s / (4.0 × 10^9 atoms × E)) × 4.0 × 10^9 atoms

Finally, we can convert the activity from Curie (Ci) to nanoCurie (nCi) by multiplying by 10^9:

Activity in nCi = A × 10^9

By following these steps, you should be able to calculate the activity of the source in nanoCurie (nCi).