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De broglie wavelength and orbits

  1. Mar 3, 2009 #1
    1. The problem statement, all variables and given/known data

    If the be Broglie wavelength associated to the first orbit of the electron inside the atom of hydrogen is 62.4 nm, what is the wavelength associated to the fourth orbit?

    1. 62.4 nm
    2. 124.8 nm
    3. 312 nm
    4. 249.6 nm

    2. Relevant equations

    # of wavelengths x n = 2pie(R)
    n= energy level
    r= radius
    lambda= h/p (i dont believe this one is necessary)
    3. The attempt at a solution

    ok i got 1. as the answer but it doesnt sound right since its the same wavelength as the first energy level am i doing something wrong?
    6.24E-8(1)= 2pieR
    9.931268449E-9= R
    # of wavelengths x 4= 2pieR
    #of wavelengths x 4= 6.283185307(9.931268449E-9)
    (do i multiply the radius by 4 since its the fourth energy level?, which is what i was assuming)
    #of wavelengths x 4= 6.283185307( 3.97250738E-8)
    # of wavelengths x 4= 2.497E-7
    # of wavelengths= 6.24E-8 m?
    is this right or am i doing something wrong
  2. jcsd
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