# Endothermic and Threshold reactions - Are they Equivalent?

• Michal Kovac
In summary: The energy needed to do this is called the "activation energy."In summary, the reaction has a Q-value of 2.8 MeV and is not a threshold reaction.
Michal Kovac
Hi,

up to this day I thought that endothermic and threshold reactions are equivalent. I mean each endothermic reaction must be threshold and each threshold reactions must be endothermic. But I think I was wrong.
Here is example (from this source Q-value):

10B(n,2*alpha)T

This threshold reaction of fast neutron with an isotope 10B is the main way, how radioactive tritium in primary circuit of all PWRs is generated. 10B is the principal source of radioactive tritium in primary circuit of all PWRs (which use boric acid as a chemical shim).

So, this is a threshold reaction and at the same time it is the exothermic reaction, because:

Using the mass-energy equivalence, the Q-value of this reaction is:

Q = {(10.0129+1.00866) [amu] – (3.01604+2 x 4.0026) [amu]} x 931.481 [MeV/amu]

= 0.00036 x 931.481 = 0.335 MeV

Is this consideration right?

I think this reaction is considered to be threshold because of its cross-section:

Figure of reaction cross-section.

But does anybody know, why the reaction cross-section have a threshold at 1.2 MeV??
Can it be derived from some reaction kinematics or it is "simply" some quantum behaviour of 10B nucleus??

Michal Kovac said:
But does anybody know, why the reaction cross-section have a threshold at 1.2 MeV??
Can it be derived from some reaction kinematics or it is "simply" some quantum behaviour of 10B nucleus??
Look at the reaction cross-section and energy for 10B(n,α)7Li and also the binding energy of 7Li <-> T + α.

What energy is necessary to dissociate 7Li into T + α?

It's a QM thing. There is both total energy (kinetic and rest mass) and momentum to consider.

I happened to stumble across this (old) question and, since the premise of the question is incorrect, I thought I should comment.

The reaction ##^{10}B(n,\alpha)^7Li## has a positive ##Q##-value (of about 2.8 MeV). This means it is exoergic (or, as it's sometimes written, exothermic -- I think either is OK). And therefore it is not a "threshold reaction," by which we universally mean that the reaction has a negative ##Q##-value. For reactions with ##Q<0## one must supply (kinetic) energy to the particles in the initial state to get the reaction to 'go.'

sirapwm said:
I happened to stumble across this (old) question and, since the premise of the question is incorrect, I thought I should comment.

The reaction ##^{10}B(n,\alpha)^7Li## has a positive ##Q##-value (of about 2.8 MeV). This means it is exoergic (or, as it's sometimes written, exothermic -- I think either is OK). And therefore it is not a "threshold reaction," by which we universally mean that the reaction has a negative ##Q##-value. For reactions with ##Q<0## one must supply (kinetic) energy to the particles in the initial state to get the reaction to 'go.'
This comment was not well constructed originally by me. The original question was about the equivalence of the terms "endothermic" and "threshold reaction" using the reaction ##^{10}B(n,2\alpha)^3H## as an example. And then I muddied the waters by using a different reaction, ##^{10}B(n,\alpha)^7Li## as an example. Sorry about this.

The answer is, "yes" -- endothermic and threshold reaction are completely equivalent. They are each statements of the fact that the reaction requires energy to proceed. Endothermic refers to the (non-zero, positive) amount of energy required in the center of mass frame. "Threshold reaction" is the same statement but the implicit, perhaps, assumption is that we're talking about the projectile energy in the lab frame.

For the reaction ##a + A \to b + B##, the center of mass energy for the threshold reaction "to go" is: ##E_c > Q##, where ##Q = m_a + m_A - (m_b + m_B)##. In the laboratory frame, where the target "A" is at rest, the projectile energy must be: $$E_a = \frac{-Q(2m_{aA} + (-Q))}{2m_A}.$$ Here, ##m_{aA} = m_a + m_A##.

I'm not sure where the figure in the OP with "##E_k > 1.2 MeV##" comes from but it is incorrect if we assume that ##E_k## is the energy of the neutron in the lab frame (with the ##^{10}B## at rest). The attachment generated here) shows that the correct value for ##Q_{^{10}B(n,2\alpha)^3H} \approx 0.322## MeV > 0, meaning it is both exothermic and not a threshold reaction.

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## 1. What is the difference between endothermic and threshold reactions?

Endothermic reactions absorb energy, while threshold reactions require a minimum amount of energy to occur.

## 2. Do endothermic and threshold reactions have the same outcome?

No, they do not. Endothermic reactions result in an increase in energy and a decrease in temperature, while threshold reactions have a specific energy threshold that must be reached for the reaction to occur.

## 3. Can endothermic reactions also have a threshold?

Yes, some endothermic reactions may have a threshold energy requirement in order to proceed.

## 4. How are endothermic and threshold reactions related?

Endothermic reactions may have a threshold energy requirement, but not all threshold reactions are endothermic. Threshold reactions are a type of reaction that is defined by the minimum amount of energy needed for the reaction to occur. Endothermic reactions, on the other hand, are defined by their absorption of energy.

## 5. Can endothermic and threshold reactions be equivalent?

No, they cannot. Endothermic and threshold reactions may have some similarities, but they are fundamentally different types of reactions. Endothermic reactions require an input of energy, while threshold reactions simply require a minimum amount of energy to proceed.