\[E_{th}=-Q\left(1+\frac{m_a}{m_A}\right)\]
Variables
Eththreshold energy (J)
Qreaction Q-value (J)
maprojectile mass (kg)
mAtarget nucleus mass (kg)
Description
What is this formula?
This formula estimates the threshold kinetic energy required for an endothermic nuclear reaction. It accounts for the negative Q-value and the recoil of the target nucleus.
When to use it
Use this formula when a nuclear reaction has Q<0 and the incoming projectile must supply enough kinetic energy for the reaction to occur.
Example
Given:
Q=-2.0×10^-13 J
ma=1.67×10^-27 kg
mA=1.00×10^-26 kg
Formula:
Eth=-Q(1+ma/mA)
Substitution:
Eth=-(-2.0×10^-13)(1+1.67×10^-27/1.00×10^-26)
Result:
Eth=2.33×10^-13 J
Applications
- Endothermic nuclear reaction analysis
- Particle accelerator calculations
- Nuclear reaction planning
- Reaction feasibility studies
- Nuclear physics education