9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

Question

9. The average diameter of an atom is 2 x 10-8 m. What if the average diameter of an atom was 1 cm? How tall would you be?

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Farah 4 years 2021-08-21T04:20:21+00:00 1 Answers 120 views 0

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  1. vankhanh
    0
    2021-08-21T04:22:05+00:00
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    Answer:

    You’d be 2 * 10^{-6} times tall

    Step-by-step explanation:

    Given

    Represent the previous and new diameter by D1 and D2;

    D_1 = 2 * 10^{-8}m

    D_2 = 1\ cm

    To determine how tall you’d be, we need to divide D2 by D1;

    Ratio = \frac{D_2}{D_1}

    Substitute values for D2 and D1

    Ratio = \frac{2 * 10^{-8}m}{1\ cm}

    Convert cm to m

    Ratio = \frac{2 * 10^{-8}m}{1 * 0.01\ m}

    Ratio = \frac{2 * 10^{-8}m}{0.01\ m}

    Convert denominator to exponents

    Ratio = \frac{2 * 10^{-8}m}{10^{-2}\ m}

    Ratio = \frac{2 * 10^{-8}}{10^{-2}}

    Apply Law of indices

    Ratio = 2 * 10^{-8} * 10^2

    Ratio = 2 * 10^{-8+2}

    Ratio = 2 * 10^{-6}

    Hence;

    You’d be 2 * 10^{-6} times tall

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