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Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 months ago

What is the speed of an electron with kinetic energy 780 eV? What is the speed of an electron with kinetic energy 0.40 keV?

A) What is the speed of an electron with kinetic energy 780 eV?

B) What is the speed of an electron with kinetic energy 0.40 keV?

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  • Anonymous
    4 months ago
    Favorite Answer

    1 ev = 1.60*10^-19 joule

    A)

    E = 780 ev = 1.25*10^-16 joule

    mass of el. m = 9.11*10^-31 kg

    speed V = √2E/m = √25*10^-17*10*31/9.11 = 10^7√25/9.11 = 1.66*10^7 m/sec

    B)

    E = 400 ev = 0.64*10^-16 joule

    mass of el. m = 9.11*10^-31 kg

    speed V = √2E/m = √12.8*10^-17*10*31/9.11 = 10^7√25/9.11 = 1.18*10^7 m/sec

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  • 4 months ago

    780 eV = 1.25e-16 J

    mass of electron is 9.1e-31 kg 

    KE = ½mV² = 1.25e-16 J

    V = √(2•1.25e-16/9.1e-31) = 1.66e7 m/s

    which is close to the speed of light, so you should use the equation below, which gets complicated.

    mc²(γ–1) = 1.25e-16

    γ–1 = 1.25e-16 / (9.1e-31)(3e8)² = 0.0015284

    γ = 1/√(1–(V²/c²)) = 1.0015284

    √(1–(V²/c²)) = 0.998474

    1–(V²/c²) = 0.9969503

    V²/c² = 0.0030497

    V/c = 0.0552244

    V = 1.656e7 m/s

    so the error is small

    second one is similar, but slower, so the first equations are fine

    Relativistic KE = mc²γ–mc² = mc²(γ–1)

    γ = 1/√(1–(V²/c²))

    Kinetic Energy in J if m is in kg and V is in m/s

    KE = ½mV²

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