Answer
The threshold energy required to initiate a specific nuclear reaction depends on the masses of the incident particle (ma) and the target nucleus (MA), as well as the Q value of the reaction. The general expression for the threshold energy (E) is given by:
E = [(MA + ma)c^2 / (MAma)] * Q
where c is the speed of light.
As the mass of the target nucleus increases, the threshold energy required to initiate the reaction decreases. This can be seen from the equation above, as the denominator (MAma) increases with increasing target mass, leading to a decrease in the overall value of the expression.
The graph of threshold energy versus target mass would look like a decreasing curve that asymptotically approaches a horizontal line as the target mass becomes much greater than the incident mass. At very large target masses, the threshold energy approaches a constant value given by:
E = Q + ma*c^2
This means that at large target masses, the minimum energy required to initiate the reaction is equal to the Q value of the reaction plus the rest energy of the incident particle. This is because the kinetic energy of the incident particle becomes negligible compared to its rest energy at very large target masses.
Physically, this means that if the mass of the target is much greater than that of the incident particle, the threshold energy required to initiate the reaction approaches a constant value. This is because the incident particle has negligible kinetic energy compared to its rest energy, and so the energy required to overcome the Coulomb barrier and initiate the reaction is dominated by the Q value of the reaction. This also implies that, for very heavy target nuclei, even low-energy incident particles can initiate nuclear reactions.
Work Step by Step
The threshold energy required to initiate a specific nuclear reaction depends on the masses of the incident particle (ma) and the target nucleus (MA), as well as the Q value of the reaction. The general expression for the threshold energy (E) is given by:
E = [(MA + ma)c^2 / (MAma)] * Q
where c is the speed of light.
As the mass of the target nucleus increases, the threshold energy required to initiate the reaction decreases. This can be seen from the equation above, as the denominator (MAma) increases with increasing target mass, leading to a decrease in the overall value of the expression.
The graph of threshold energy versus target mass would look like a decreasing curve that asymptotically approaches a horizontal line as the target mass becomes much greater than the incident mass. At very large target masses, the threshold energy approaches a constant value given by:
E = Q + ma*c^2
This means that at large target masses, the minimum energy required to initiate the reaction is equal to the Q value of the reaction plus the rest energy of the incident particle. This is because the kinetic energy of the incident particle becomes negligible compared to its rest energy at very large target masses.
Physically, this means that if the mass of the target is much greater than that of the incident particle, the threshold energy required to initiate the reaction approaches a constant value. This is because the incident particle has negligible kinetic energy compared to its rest energy, and so the energy required to overcome the Coulomb barrier and initiate the reaction is dominated by the Q value of the reaction. This also implies that, for very heavy target nuclei, even low-energy incident particles can initiate nuclear reactions.
