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23 September, 23:12

The nucleus of a hydrogen atom is a single proton, which has a radius of about 1.2 * 10-15 m. The single electron in a hydrogen atom orbits the nucleus at a distance of 5.3 * 10-11 m. What is the ratio of the density of the hydrogen nucleus to the density of the complete hydrogen atom?

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  1. 24 September, 00:40
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    Answer: 0.86 * 10^14

    Explanation:

    Given the following:

    Radius of proton = 1.2 * 10-15 m

    Radius of hydrogen atom = 5.3 * 10-11 m

    Density of proton could be calculated thus:

    Mass of proton = 1.67 * 10^-27 kg

    Using the formula:

    (4/3) * pi * r^3

    (4/3) * 3.142 * (1.2 * 10^-15) ^3 = 7.24 * 10^-45

    Density = mass / volume

    Density = (1.67 * 10^-27) / (7.24 * 10^-45)

    = 0.2306 * 10^18

    Density of hydrogen atom:

    Mass of hydrogen atom = 1.67 * 10^-27 kg

    Using the formula:

    (4/3) * pi * r^3

    (4/3) * 3.142 * (5.3 * 10^-11) ^3 = 6.24 * 10^-31

    Density = mass / volume

    Density = (1.67 * 10^-27) / (6.24 * 10^-31)

    = 0.2676 * 10^4

    Ratio is thus:

    Density of proton / density of hydrogen atom

    0.2306 * 10^18 / 0.2676 * 10^4 = 0.8617 * 10^14
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