The de Broglie wavelength

  1. The mass of an electron is 9.11*10^-31 kg. If the de Broglie wavelength for an electron in an hydrogen atom is 3.31*10^-10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00*10^8 m/s.

    here's what I did: i solved for velocity=6.626*10^-34J/(9.11*10^-31kg)(3.31*10^-10)
    and i tried to gain the percent by dividing the speed of light by velocity.

    where did i go wrong?
  2. jcsd
  3. cepheid

    cepheid 5,194
    Staff Emeritus
    Science Advisor
    Gold Member

    Your calculation is wrong. Don't just blindly do calculations. Think...does the number your calculator has spewed out actually make any sense? When it's something ridiculous like 10^-74 m/s, the answer is emphatically NO. Kind of slow for a particle, don't you think?

    I get v = (0.00732)c

  4. how did u calculate.... watch the exponents first......

    the magnitude is 10^7 m/s...

    [tex]\frac{6}{9\times3}\times\frac{10^{-34}}{10^{-31}\times10^{-10}}\approx\frac{2}{9}10^7 m/s[/tex]
    this suggest us that it is better to treat the electron relativistically if we want to penetrate deep in its properties...
  5. thanx Dirac :)
  6. so hows do i get the percentage here's what i'm doing: 3.00*10^8 m/s /100 = 0.00732/x. x=2.4*10^8, but i know this isn't right so, what shall i do?
  7. cepheid

    cepheid 5,194
    Staff Emeritus
    Science Advisor
    Gold Member

    I'm not sure what percentage you are talking about, since it's not mentioned in the original post.

    For the velocity of the particle, I get:

    [tex] v = 2.197 \times 10^6 \ \ \ \frac{\textrm{m}}{\textrm{s}} [/tex]

    The question asks how fast the particle is moving relative to the speed of light. Well, their ratio is

    [tex] \frac{v}{c} = \frac{2.197 \times 10^6 \ \ \ \textrm{m/s}}{3.00 \times 10^8 \ \ \ \textrm{m/s}} = 0.00732 [/tex]

    So, expressed in units of the speed of light, the velocity is

    [tex] v = 0.00732c [/tex]

    The particle is moving at 0.00732 times the speed of light. Obviously, as a percentage, that's 0.732%. So I guess if you wanted to, you could say that the particle is moving at 0.732% of the speed of light. It's a completely equivalent statement though. It doesn't add any extra meaning.
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