Using Planck’s constant as h = 6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of a proton is 1.66 E

Question

Using Planck’s constant as h = 6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of a proton is 1.66 E-27 kg. Remember to identify your data, show your work, and report the answer using the correct number of significant digits and units.

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2022-05-14T05:56:17+00:00 2 Answers 0

Answers ( 2 )

  1. Ada125lyn
    0
    2022-05-14T05:57:29+00:00

    We can solve the problem by using De Broglie’s relationship:
    [tex]p= mv= frac{h}{lambda} [/tex]
    where
    p is the momentum of the particle
    m is the the mass
    v is the velocity
    h is the Planck constant
    [tex]lambda[/tex] is the wavelength of the particle

    By re-arranging the equation, we get
    [tex]lambda = frac{h}{mv} [/tex]
    and by using the data about the proton mass and speed, we find its wavelength:
    [tex]lambda= frac{6.6 cdot 10^{-34} Js}{(1.66 cdot 10^{-27} kg)(5.0 cdot 10^6 m/s)}=7.95 cdot 10^{-14} m [/tex]

  2. Amara
    0
    2022-05-14T05:58:02+00:00

    The wavelength is indirectly proportional to the mass and velocity of the particle. The wavelength of the given proton is [tex]7.95 times 10^{-14}[/tex].

    From de Broglie’s relationship:

    [tex]lambda = dfrac h{mv}[/tex]

    Where,

    [tex]m[/tex] – mass = [tex] 1.66 times 10^{-27}rm kg [/tex]

    [tex]v[/tex] – velocity = [tex]5.0 times 10^6 rm m/s[/tex]

    [tex]h[/tex] – Planck constant = [tex] {6.6times 10^{-34}}rm Js[/tex]

    [tex]lambda [/tex] – wavelength of the particle = ?

    Put the values in the formula,

    [tex]lambda = dfrac {6.6times 10^{-34}}{(1.66times 10^{-27})(5.0 times 10^6)}nlambda = 7.95 times 10^{-14}[/tex]

    Therefore, the wavelength of the given proton is [tex]7.95 times 10^{-14}[/tex].

    Learn more about De Broglie’s relationship:

    https://brainly.com/question/8752907

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