Why doesn't calculating the de Broglie wavelength work with h in eV·s?I'm trying to calculate the de Broglie wavelength of a particle with a known momentum p = 980.93 G e V / s . The de Broglie relation is: λ = h p but I notice that if I use the value of 4.136 × 10 − 15 e V ⋅ s for the Planck's constant, the answer that I get from the equation is in units of s 2 , not m. Specifically: λ = 4.136 × 10 − 15 e V ⋅ s 980.93 G e V / s = 4.25 × 10 − 27 s 2 which is not at all equivalent to the value that one gets when using h = 6.626 × 10 − 34 J ⋅ s instead (since J ⋅ s can be converted into k g ⋅ m 2 s 2 ⋅ s ). λ = 6.626 × 10 − 34 k g ⋅ m 2 s 2 ⋅ s 5.237 × 10 − 16 k g ⋅ m s = 1.27 × 10 − 18 m What's going on here?

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Why doesn&#039;t calculating the de Broglie wavelength work with h in eV·s?I&#039;m trying to calculate the de Broglie wavelength of a particle with a known momentum   p  =  980.93        G    e    V        /        s  . The de Broglie relation is:  λ  =      h    p  but I notice that if I use the value of   4.136  ×      10          −      15              e    V    ⋅      s   for the Planck&#039;s constant, the answer that I get from the equation is in units of             s        2  , not m. Specifically:  λ  =            4.136      ×              10                  −          15                            e        V            ⋅              s                    980.93                    G        e        V                    /                    s              =  4.25  ×      10          −      27                    s        2  which is not at all equivalent to the value that one gets when using   h  =  6.626  ×      10          −      34              J    ⋅      s   instead (since       J    ⋅      s   can be converted into                     k        g            ⋅                        m                2                            s            2        ⋅      s  ).  λ  =            6.626      ×              10                  −          34                                                        k            g                    ⋅                                    m                        2                                                s                    2                    ⋅              s                    5.237      ×              10                  −          16                                                  k            g                    ⋅                      m                                    s                      =  1.27  ×      10          −      18              m  What&#039;s going on here?

cegielnikmzjkf · Accepted Answer

You&#039;re running into trouble because in order to give momentum units of energy, you&#039;re setting the speed of light equal to 1,   c  =  1. If you keep the units of   c the momentum should be given in units of   eV      /    c. By dimensional analysis you can check for yourself that eV/s does not have units of momentum (kg  ⋅m/s).Therefore, in your case the momentum is actually given by   p  =  980.93     GeV      /    c which yields  λ  =            4.136      ×              10                  −          15                    eV      ⋅      s              980.93            GeV              /            c        =            4.136      ×              10                  −          15                    eV      ⋅      s      ⋅      2.99      ×              10        8            m/s              980.93            GeV        =  1.27  ×      10          −      18          m  .

motorinum6fh9v · Accepted Answer

The momentum   P is not homogeneous to eV/s but to eV.s/m which one can remember using the equation :      P    0    =      E    c  Where       P    0   is the time component of the quadri-momentum,   E the energy of the particle and   c the speed of light.

Why doesn't calculating the de Broglie wavelength work with h in eV·s? I'm trying to calculate the

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