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Today, 03:06

Through how many volts of potential difference must an electron, initially at rest, be accelerated to achieve a wave length of 0.27nm? A) 4.6 V

B) 0.046 V

C) 0.27 V

D) 4.6 MV

E) 4.6 kV

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  1. Today, 03:12
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    20.7 volts

    Explanation:

    m = mass of electron = 9.1 x 10⁻³¹ kg

    λ = wavelength of electron = 0.27 x 10⁻⁹ m

    v = speed of electron

    Using de-broglie's hypothesis

    λ m v = h

    (0.27 x 10⁻⁹) (9.1 x 10⁻³¹) v = 6.63 x 10⁻³⁴

    v = 2.7 x 10⁶ m/s

    ΔV = Potential difference through which electron is accelerated

    q = charge on electron = 1.6 x 10⁻¹⁹ C

    Using conservation of energy

    (0.5) m v² = q ΔV

    (0.5) (9.1 x 10⁻³¹) (2.7 x 10⁶) ² = (1.6 x 10⁻¹⁹) ΔV

    ΔV = 20.7 volts
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