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26 September, 12:35

2) Of the following, which has the shortest de Broglie wavelength? A) an airplane moving at a velocity of 300 mph B) a helium nucleus moving at a velocity of 1000 mph C) a nitrogen molecule moving at a velocity of 1000 mph D) a nitrogen molecule moving at a velocity of 5000 mph

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  1. 26 September, 15:53
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    B) a helium nucleus moving at a velocity of 1000 mph

    Explanation:

    According to the De Broglie relation

    λ = h/mv

    h = planks constant

    m = mass of the body

    v = velocity of the body.

    As we can see from De Broglie's relation, the wavelength of matter waves depends on its mass and velocity. Hence, a very small mass moving at a very high velocity will have the greatest De Broglie wavelength.

    Of all the options given, helium is the smallest matter. A velocity of 1000mph is quite high hence it will have the greatest De Broglie wavelength.
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