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Homework Help: De Broglie wavelength of a neutron

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the de Broglie wavelength of a neutron whose kinetic energy is equal to the average kinetic energy of a gas of neutrons at temperature T = 17 K?


    2. Relevant equations
    lambda = h/p = h/mv.


    3. The attempt at a solution

    Well first I tried taking the h = 6.63E-34 Jxs and dividing it by the mass times the square root of T = 17 K

    Thus,

    (6.63E-34)/(1.6E-27 kg)(sqrt(17)) x (1E9 m) = 100.500 nm.

    I did this because we know from kinetic theory that T is proportional to the root mean square velocity v in the gas, so that v scales as sqrt(T). This means that the momentum scales in the same way, while the wavelength as 1/sqrt(T).

    I'm not sure where to go from here, since the answer is not correct. =/
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 7, 2010 #2


    If you look at the units alone you can see that the formula has some problems.
    What are the units for sqrt(17K)? (I suppose you mean 17K)
    It is true that v is proportional with sqrt(T) but it is not equal to this.
    You need to take the complete formula for v (or p) from the kinetic theory of gases to get the right units (and the right answer, maybe).

    You can start with KE= 3/2 kB*T where KE is the average kinetic energy.
     
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