What is the velocity of the electron in He+?

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  • NCS
    Lv 7
    4 weeks ago

    For the nth orbital, the energy is

    E(n)=Z² * q⁴ * m / 8ε₀²n²h²

    and

    E = ½mv²

    so

    ½mv² = Z² * q⁴ * m / 8ε₀²n²h²

    means that

    v² = 2 * Z² * q⁴ * m / 8ε₀²n²h²

    v = Z*q² / 2ε₀nh

    Z = atomic # = 2

    q = electron charge

    ε₀ = 8.85e-12 C²/N·m²

    n = state number (assumed 1, lowest energy orbital)

    h = Planck's constant = 6.626e-34kg·m²/s

    so

    v = 2*(1.6e-19C)² / 2*8.85e-12C²/N·m²*1*6.626e-34kg·m²/s

    v = 4.4e6 m/s

    just over 1% of c

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