1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Nuclear physics problem - energy of reaction

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data
    To activate the reaction ##(n,\alpha)## with stationary ##B^{11}## nuclei, neutrons must have the activation kinetic energy ##T_{th}=4\,MeV##. ##(n,\alpha)## means that ##n## is bombarded to obtain ##\alpha##. Find the energy of this reaction.

    (Ans: ##Q=-11/12 T_{th}##)

    2. Relevant equations



    3. The attempt at a solution
    The reaction taking place is:
    $$n+B^{11}\rightarrow B^{12}\rightarrow A^{8}+\alpha$$
    From conservation of energy
    $$T_{th}=Q+T_A+T_{\alpha}\,\,\,\,\,(*)$$
    where ##T## is used to denote the kinetic energy.
    Also, from conservation of linear momentum, ##p_{A}=p_{\alpha} \Rightarrow p_{A}^2=p_{\alpha}^2 \Rightarrow m_AT_A=m_{\alpha}T_{\alpha}\,\,\,(**)##.

    From (*) and (**), I get:
    $$T_{th}=Q+T_A\left(1+\frac{m_A}{m_{\alpha}}\right)$$
    I still need one more equation. :confused:

    Any help is appreciated. Thanks!
     
  2. jcsd
  3. Feb 24, 2014 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have 4 MeV plus the rest masses of the reactants on one side, and something comparable for the products on the other.
     
  4. Feb 24, 2014 #3
    Sorry but I can't understand where are you trying to hint at. :confused:
     
  5. Feb 24, 2014 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    When I look up the masses of the reactants and the products, I get a nice imbalance. What happens with the 'disappearing' mass ?
     
  6. Feb 24, 2014 #5
    Are you talking about the mass defect? But I don't have the nuclear masses of A and B, if I had the nuclear masses, won't it be trivial to find Q?
     
    Last edited: Feb 24, 2014
  7. Feb 25, 2014 #6

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have a point there. Didn't work for me either, anyway: I ended up with -5.6 MeV/c2 .

    Other question: what about the initial momentum of the neutron ? Your conservation is only valid in the center of mass.
     
  8. Feb 25, 2014 #7
    What is A here? B is boron, Z number = 5. Upon emitting the alpha particle, the Z number must be 3, which makes the element Lithium. Lithium-8 is unstable, with its half life less than 1 second.

    I do not even think there is an element whose symbol is just A.

    Secondly, should you not assume that the new element, whatever it is, is stationary?
     
  9. Feb 25, 2014 #8

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I wonder if it could be that they are asking for the "activation energy of the reaction" which is different from the "activation kinetic energy of the neutron".

    When the neutron first enters the B11 nucleus, you get an excited B12 nucleus. Only a portion of the initial KE of the neutron goes into excitation energy, the rest is wasted as recoil KE of the B12. The activation energy of the reaction is the minimum excitation energy that will lead to the final reaction to Li8 and the alpha particle.
     
  10. Feb 25, 2014 #9
    The new particle ##B^{12}## won't be stationary. But if I were to consider its motion in linear momentum conservation, I don't know about the motion of new particles i.e the question doesn't state in which direction the two new particles fly off. :confused:

    And yes, I know its boron and lithium but I don't think its necessary to specify them for the given problem. :rolleyes:
     
  11. Feb 25, 2014 #10

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes. That's why only some of the kinetic energy of the neutron is effective in initiating the reaction.

    Not sure why you are worried about this. I think all you need to consider is how much of the kinetic energy of the neutron is converted into "internal energy" as the B11 nucleus absorbs the neutron to momentarily become a B12 nucleus.

    You might want to imagine the collision in the center of mass frame.

    OK. Basically all you need to know is that the target nucleus has 11 nucleons (if I am interpreting the problem correctly).
     
  12. Feb 25, 2014 #11
    Do I have to find this internal energy? If so, how? :confused:

    Are you talking about the conservation of linear momentum? :confused:
     
  13. Feb 25, 2014 #12

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Recall your happy days with collisions in elementary mechanics. If a block of mass m collides with a block at rest of mass M so that they become one block (at least momentarily), what fraction of the initial KE remains? What fraction of the initial KE is converted to some other form of energy of the two-block system?

    Momentum is conserved in both the lab frame and the center of mass frame. But going to the center of mass frame makes it clear how much energy gets converted into internal energy. The center of mass frame is also the frame in which the total momentum is zero.
     
  14. Feb 25, 2014 #13
    Since the momentum is conserved, I can write: ##p_n=p_{B^{12}} \Rightarrow m_nT_{th}=12m_nT_{B^{12}}##
    $$\Rightarrow T_{B^{12}}=\frac{T_{th}}{12}$$
    This is the kinetic energy of ##B^{12}## nucleus. The energy lost is ##(11/12)T_{th}##. Though this matches with the given answer but I don't see why this should the answer. :confused:
     
  15. Feb 25, 2014 #14

    TSny

    User Avatar
    Homework Helper
    Gold Member

    I'm not positive I'm interpreting the problem correctly. But think of it this way. Suppose you had a block of mass m that is going to collide with a block at rest of mass 11m that has a spring as shown. Suppose that if the spring becomes fully compressed, the system explodes. Thus, there is a certain "activation energy" that the spring must absorb before we get an explosion ("reaction").

    If you are told that the minimum kinetic energy that the small block must have initially to get an explosion is To, then you can work out the "activation energy" for the reaction.
     

    Attached Files:

  16. Feb 25, 2014 #15
    This "activation energy" is the potential energy stored in the spring, right?

    But I really don't see how to carry this analogy in the given problem. I have the energy lost and final energy of the B^(12) nucleus but what to do with them. :confused: :cry:
     
  17. Feb 25, 2014 #16

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes.

    If the initial KE of the neutron is below 4 MeV, then the specified reaction doesn't occur. This is because not enough energy is transferred into "internal energy" (analogy: potential energy of the spring). My interpretation of the question is that they are just asking for the minimum value of the increase in internal energy in order for the reaction to "go".

    It is very much like activation energy for some chemical reactions. There must be a certain input of energy before the reaction will go. This is different from the energy released in the reaction. Two different chemical reactions could have the same activation energy, but release very different amounts of energy.
     
  18. Feb 25, 2014 #17

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Where does the "energy lost" go? Where did it go in the block analogy?
     
  19. Feb 25, 2014 #18
    If there were no spring, then in an inelastic collision, energy wasted gets converted in heat or some other form of energy, I guess in the spring case, it gets converted into the potential energy of spring?
     
  20. Feb 25, 2014 #19

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes. Anyway, my interpretation is that they want this "spring" energy.
     
  21. Feb 25, 2014 #20
    Thanks a lot TSny! :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Nuclear physics problem - energy of reaction
  1. Nuclear Reactions (Replies: 6)

Loading...