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12 February, 09:41

The de Broglie equation relates the wavelength and the kinetic energy of particles. What is the wavelength, in nanometers, associated with an electron with a speed of 3.42 * 106 m/s? The mass of an electron is 9.109 * 10-31 kg.

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  1. 12 February, 10:06
    0
    Answer:2.1*10^-9 m or 2.1nm

    Explanation:

    According to De Broglie's equation, the wavelength of any particle is given by wavelength = h/MV

    6.6*10^-34/9.109*10^-31*3.42*10^-6

    = 2.1*10^-9 m
  2. 12 February, 10:07
    0
    0.213 nm

    Explanation:

    The equation of de Broglie that relates the energy and the wavelength is:

    E = h*f

    Where h is the plack constant (6.626x10⁻³⁴ J. s), and f is the frequency. The frequency is the speed of light (c) divided by the wavelength (λ).

    The wavelength can be calculated then by:

    λ = h/mv

    Where m is the mass, and v the velocity of the particle. So:

    λ = 6.626x10⁻³⁴ / (9.109x10⁻³¹x3.42x10⁶)

    λ = 2.13x10⁻¹⁰ m

    λ = 0.213 nm
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