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9 August, 14:39

Calculate the density of a proton, given that the mass of a proton is 1.0073 amu and the diameter of a proton is 1.73 * 10 ^ - 15 m. The answer should be in g/cm^3

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  1. 9 August, 18:03
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    Density = 6.17 * 10^14 g/cm³

    Explanation:

    Given Parameters

    Mass of the proton = 1.0073 amu

    Diameter of the proton = 1.75 * 10^-15 m

    Required:

    Calculate the density of the proton.

    Density is calculated using the following formula;

    Density = mass / volume

    Where mass should be in grams and volume should be in cm ³

    Calculating mass of a proton in grams.

    Mass = 1.0073 amu

    First, we convert to kilogram

    Mass = 1.0073 * 1.66054 * 10^-27 kg

    Then we convert to grams

    Mass = 1.0073 * 1.66054 * 10^-27 * 10³ g

    Mass = 1.0073 * 1.66054 * 10^-24 g

    Mass = 1.673 * 10^-24 g

    Then we calculate the volume of the proton

    Volume = 4/3πR³ where R = Radius

    And R = ½d.

    First calculate the radius in centimetres

    R = ½ * 1.73 * 10^-15 m

    R = 0.865 * 10^-15

    Convert to centimetres

    R = 0.865 * 10^-15 * 10² m

    R = 0.865 * 10^-13 cm

    So, Volume = 4/3 * 3.14 * (0.865 * 10^-13) ³

    Volume = 4.187 * (0.865 * 10^-13) ³

    V = 4.187 * 0.865³ * 10^-39

    V = 2.71 * 10^-39cm³

    So, density = Mass / Volume becomes

    Density = 1.673 * 10^-24 g / 2.71 * 10^-39cm³

    Density = 0.617 * 10^15 g/cm³

    Density = 6.17 * 10^14 g/cm³
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