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16 November, 10:08

Consider two straight wires lying on the x-axis, separated by a gap of 4 nm. The potential energy in the gap is about 3 eV higher than the energy of a ondu tion ele tron in either wire. What is the probability that a ondu tion ele tron in one wire arriving at the gap will pass through the gap into the other wire?

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  1. 16 November, 10:59
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    Answer: 1.3 * 10^-31

    Explanation:

    the required probability is P = e^ (-2αL)

    Firstly, evaluate (-2αL)

    α = 1/hc √2mc^2 (U - E)

    h = modified planck's constant

    where,

    (-2αL)

    = - (2L) / (h/2π) * √2mc^2 (U - E)

    = - (2L) / (hc^2/π) * √2mc^2 (U - E)

    (hc^2/2pi) = 197*eV. nm (standard constant)

    2*L = 8 nm

    mc^2 = 0.511*10^6 eV

    Where m = mass electron

    C = speed of light

    (-2αL) = [-8nm / (197 eV. nm) ] * (1.022 * 10^6 eV**3 eV) ^0.5

    (-2αL) = - 71.1

    Probability = e^ (-2αL) = e^-71.1 = 1.3 * 10^-31

    Therefore, the probability that a ondu tion ele tron in one wire arriving at the gap will pass through the gap into the other wire 1.3 * 10^-31.
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