Find the threshold energy that the incident neutron must have to produce the reaction
1 n 0 + 4 He 2---> 2 H 1 + 3 H 1
For this, like the 1 n 0<--- it is supposed to be written like 1 on the top 0 on the bottom next to n. like the atomic number of neutron and the other elements.
You will need to look up the masses of each of those particles. There will be slightly more mass on the right side, since energy is needed to make the reaction happen. Call the meass difference "delta M"
The threshold incident neutron energy, from the Einstein E=mc^2 law, is
E = c^2 * (delta M)
That is the energy required in "center of mass"-fixed coordinates. Since the neutron is moving and the helium nucleus is fixed in the lab coordinate system, a somewhat higher nuetron energy will be required, in order for the energy available in a coordinate system fixed with the center of mass to equal E. The initial speed of the neutron in CM system will be 4/5 of the speed in lab coordinates
To find the threshold energy for the incident neutron to produce the given reaction, we need to calculate the mass difference (delta M) between the reactants and the products.
First, we need to look up the masses of the particles involved in the reaction from a periodic table or a database. The masses are given in atomic mass units (amu).
The masses are:
neutron (n): 1.008665 amu
helium-4 (He): 4.002603 amu
proton (H): 1.007825 amu
Now let's calculate the mass difference (delta M) between the reactants and the products:
Reactants: 1 n 0 + 4 He 2
Products: 2 H 1 + 3 H 1
Reactant mass = (1.008665 amu) + (4.002603 amu) = 5.011268 amu
Product mass = (2 * 1.007825 amu) + (3 * 1.007825 amu) = 5.0392 amu
Delta M = Product mass - Reactant mass = 5.0392 amu - 5.011268 amu = 0.027932 amu
The threshold incident neutron energy can be calculated using the Einstein's mass-energy equivalence equation E = mc^2, where E is the energy, m is the mass difference, and c is the speed of light.
E = c^2 * (delta M)
E = (3.00 × 10^8 m/s)^2 * (0.027932 amu)
Now, amu is not a standard unit of mass used in calculations, so we need to convert it to kilograms. 1 amu is approximately equal to 1.66 × 10^-27 kg.
E = (3.00 × 10^8 m/s)^2 * (0.027932 amu * 1.66 × 10^-27 kg/amu)
After converting amu to kg, the threshold incident neutron energy can be calculated.