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3 March, 19:34

A particle has a mass of 2 * 10-30 kg and an uncertainty in its velocity of 102 m/s. What is the minimum possible uncertainty in position that the particle can have so as not to violate the uncertainty principle?

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  1. 3 March, 19:46
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    m = mass of the particle = 2 x 10⁻³⁰ kg

    Δv = uncertainty in velocity of the particle = 10² m/s

    Δx = uncertainty in position of the particle = ?

    h = plank's constant = 6.63 x 10⁻³⁴ J-s

    uncertainty principle is given as

    m Δx Δv ≥ h / (4π)

    inserting the values

    (2 x 10⁻³⁰) Δx (10²) ≥ (6.63 x 10⁻³⁴) / (4 (3.14))

    Δx ≥ 2.64 x 10⁻⁷ m

    so minimum possible uncertainty is 2.64 x 10⁻⁷ m
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