(a) Assume an electron in the ground state of the hydrogen atom moves at an average speed of 5.00 × 106 m/s. If the speed is known to an unc

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(a) Assume an electron in the ground state of the hydrogen atom moves at an average speed of 5.00 × 106 m/s. If the speed is known to an uncertainty of 1 percent, what is the minimum uncertainty in its position

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Diễm Kiều 4 years 2021-08-12T15:38:16+00:00 1 Answers 38 views 0

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  1. Euphemia
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    2021-08-12T15:39:57+00:00
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    Answer:

    The minimum uncertainty in its position is 1.1587 nm

    Explanation:

    Given;

    average speed of electron, v = 5.00 × 10⁶ m/s

    percentage of speed uncertainty = 1%

    Δv = 0.01( 5.00 × 10⁶ m/s) = 5.00 × 10⁴ m/s

    Applying Heisenberg’s uncertainty principle, to determine the uncertainty in its position.

    ΔxΔP ≥ h/4π

    Δx(mΔv)  ≥ h/4π

    Δx = h/4πmΔv

    where;

    Δx is uncertainty in its position

    h is Planck’s constant

    m is mass of electron

    Δx ≥ \frac{6.626 *10^{-34}}{4\pi *9.1*10^{-31}*5*10^4} = 1.1587*10^{-9} \ m

    Δx ≥ 1.1587 nm

    Therefore, the minimum uncertainty in its position is 1.1587 nm

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