The De Broglie Wave Equation

  1. Hi,
    I recently came across a proof for the De Broglie wave equation in a book, which went as follows:
    E of photon = mc2
    = m*c*c
    = (m*c)c
    = (p)c ( ie - momentum*speed of light)
    = (p)(f*lamda)
    Therefore, hf = p(f*lambda)
    Therefore, p = hf/ f*lambda
    = h/lambda.
    Therefore, Lambda (ie- wavelength) = h/ mv.

    However, I'm not sure if I agree with this, so I wanted to ask a few questions. Firstly, it is true that the energy of a photon = hf, but I dont think that it should equal mc2. After all, this Einsteinian equation literally means energy produce = mass destroyed*speed of light. So, what mass has been destroyed to create the energy of the photon? Furthermore, how can we take mc to be the momentum of the photon, if this is mass destroyed, not mass of the photon?
    As slightly different question, what exactly is the wavelength of a particle? If the wavelength of a wave is "the distance between two crests or adjacent points", then what is the wavelength of a particle?
    Thanks is advance. :-D
  2. jcsd
  3. jcsd

    jcsd 2,226
    Science Advisor
    Gold Member

    Really tou need the equation:

    [tex]E^2 = m_0^2c^4 + p^2c^2[/tex]

    As a photon has zero mass:

    [tex]E = pc[/tex]

    In your book they've defined m as relativistic mass.
  4. I've had a think and could you say that, since if you accelerate and object and it gains XJoules of KE it will gain X/c2 kg of mass, that in creating the photon you have "destroyed" some mass and thus that the photon must have mass? It must do so that when it gives its energy to something else, that thing will gain energy AND mass.
  5. jcsd

    jcsd 2,226
    Science Advisor
    Gold Member

    The photon doesn't have mass as mass is usually defined as the rest mass.
  6. The verificiation of the De Broglie formula (I am lead to believe) comes from considering a de Broglie wave:
    [tex]$\psi ({\bf{r}},t) = Ae^{i({\bf{k}}.{\bf{r}} - \omega t)} $

    If you assume the relationshup [tex]E = \hbar \omega [/tex] holds for material particles you then write [tex]E = \hbar \omega = \frac{{m_0 c^2 }}{{\sqrt {1 - \beta ^2 } }}[/tex], use this in the group velocity formula and obtain the required result.

    However to show that [tex]E = \hbar \omega [/tex] is a consitent step, you show the invariance of the quantity [tex]kr - \omega t
    [/tex] in two inertial frames S and S'.
    Last edited: Jun 20, 2004
  7. sorry, there is mass/energy and it is conserved. A photon has mass/energy and it may be expressed as mass or frequency. E=hn=mCC
  8. Just consider that all physics equations : E = mc2 ; E = hf ; Gij = Tij; can be expressed in a single way depending on th scale. This single law is :

    extensity flux = diffusivity * extensity concentration gradient.
  9. malawi_glenn

    malawi_glenn 4,727
    Science Advisor
    Homework Helper

    this thread is 5years old..
  10. The mass of a photon is: m=hn/CC; planks constant times the frequency divided by the speed of light squared.
    Mass is mass; mass times accelleration is force but for a photon accelleration is defined as CC ie. C squared. Thus F=mCC.
  11. malawi_glenn

    malawi_glenn 4,727
    Science Advisor
    Homework Helper

    sammy, this is one of the most discussed things in this forum, Please read the thread that was suggested to you.

    Now, WHERE and WHY should the acceleration of a photon be defined in that way? There is no reason and meaning to that, c^2 does not even have the units of acceleration.

    sammy, there equation is [itex]E=m c^2[/itex], where [itex]m = \gamma m_0[/itex] and [itex]\gamma = 1/\sqrt{1-v^2/c^2}[/itex].

    The equation [itex]E=m c^2[/itex] can also be written as [itex]E^2 = (pc)^2 + (m_0c^2)^2[/itex].

    The energy of a photon is [itex]E = \hbar \omega[/itex]

    Now, try to fit the photon-energy equation to make [itex] \hbar \omega = mc^2 [/itex]... and you will find:

    [itex]E = \hbar \omega = mc^2 = \gamma m_0c^2[/itex] now the rest mass of the photon is zero, and \gamma for the photon is infinite, since the photon moves at c. So what happened to the photon mass?

    we have that [itex]m = m_0 \gamma = 0 \times \infty [/itex] .. nice

    BUT this is nice, since m_0 = 0:

    [itex]E^2 = (pc)^2 \rightarrow [/itex]
    [itex]p = E/c[/itex]
    Last edited: Mar 21, 2009
  12. I agree with you, cc has not the unit of acceleration. But cc/l with "l" being wave length has the unit of acceleration. it is then easy to make de broglie and einstein equations equivallent.
  13. malawi_glenn

    malawi_glenn 4,727
    Science Advisor
    Homework Helper

    in what sense is deBroigle and "Einstein equation" equivalent?
  14. They are the same mathematical description of the quantic reality. And you can not imagine how Sammy is close to the final solution when he writes F = m cc !!
  15. malawi_glenn

    malawi_glenn 4,727
    Science Advisor
    Homework Helper

    Sorry dude, but you have to refer to accepted science, published in peer review journals, not your own opinions and idea what "quantic reality" is etc.

    Force is instantaneous change momentum also, so there is in the first place no need for an equation of the kind F = mc^2, since F = dp/dt will work too, using p = E/c for a photon.
  16. ok I stope. But there is no fault when you are doing true calculations directly. You do it yourself F = dp/dt... I can do for example E/V = P (Pa) = mc2/V = mc2/S.l et c2/l (m.s-2) = S/m * P
  17. cristo

    cristo 8,394
    Staff Emeritus
    Science Advisor

    This thread is from 5 years ago. There is no need to dredge up something that old, thus I am locking this.
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook