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E = hf for electron. Why?

  1. Oct 13, 2012 #1
    I came across a problem my teacher assigned. We are asked to calculate frequency of electron having certain energy. My teacher used E = hf to solve the problem. I thought that could only be applied to photon. Is it because electron has wave-like nature and has quantized energy?
    Last edited: Oct 13, 2012
  2. jcsd
  3. Oct 13, 2012 #2
    Okay . You need to clear your fundamentals from your teacher.
    E=hf. does not give the energy of electron. It gives the enegy required / released when electrons change their energy levels. And this enegy may be radiated in the form of photons or by heat or any other form.

    I recommend you to go through Bohr's postulates regarding Atomic model.
  4. Oct 13, 2012 #3
    The question is given like this:
    electron has 511keV and kinetic energy of 100 MeV and determines its frequency.
    the answer is 2.43*10^22 Hz, which can be determined through f = E/h.

    I just wonder how can my teacher use the equation like that for such straightforward question.
  5. Oct 13, 2012 #4
    It's the frequency corresponding to the electron's De Broglie wavelenght. E = 100.511 MeV, f = E/h.
  6. Oct 13, 2012 #5


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    It is a quantum-mechanical frequency, and the connection between energy and frequency is the same for all particles.
  7. Oct 13, 2012 #6


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    E=hf is fine for describing the energy associated with a photon but I am not familiar with assigning frequency to energy for a particle. There is a relationship between wavelength (de Broglie) and momentum for particles (P=h/λ) but where does a constant relationship between Energy and Frequency for particles come in? Where would that leave the equation for waves 'c=fλ' for instance?
    What am I missing here?
  8. Oct 13, 2012 #7


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    This comes from relativistic wave equations - but even in the "classic" case, an electron with 100 MeV kinetic energy has E≈pc=hc/λ=hcf/v≈hf.
    Last edited: Oct 13, 2012
  9. Oct 13, 2012 #8
    We can connect E = hf for an electron to the Schrödinger equation for matter waves by examining the time dependency of a stationary state.

    [itex]| \Psi (t)> = e^{-iE_{n}t/\hbar}| n>[/itex]

    Where |n> represents a stationary (stable) state at time zero, and En represents the energy of that state. Now, if we substitute into the above equation the following:

    [itex]E_{n} = hf = \hbar \omega = \hbar 2\pi f[/itex]

    Then, we'd get

    [itex]| \Psi (t)> = e^{-i2\pi ft}| n >[/itex]

    Notice that the exponential multiplying the stationary state has a frequency of magnitude [itex]f[/itex]. So the phase of a stationary state of a matter wave (from Schrödinger's equation) cycles at a frequency given by the energy of the state and the equation E = hf.
    Last edited: Oct 13, 2012
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