Suppose you built a scale-model atom in which the nucleus is the size of a tennis ball. About how far would the cloud of electrons extend?

Question

Suppose you built a scale-model atom in which the nucleus is the size of a tennis ball. About how far would the cloud of electrons extend?

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Philomena 5 months 2021-08-11T10:58:17+00:00 1 Answers 3 views 0

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    2021-08-11T10:59:59+00:00

    Answer:

    500 m

    Explanation:

    The size of a nucleus is about

    d=10^{-15} m

    Instead, the size of the electron cloud extends at the order of

    D=10^{-10}m

    This means that the ratio between the size of the electron cloud and the size of the nucleus is about

    k=\frac{D}{d}=10,000

    So, the electron cloud is about 10,000 bigger than the nucleus of the atom.

    Here we want to build a scale-model atom, in which the nucleus is the size of a tennis ball, so a size of approximately

    d=5 cm

    Therefore, since the proportions must be respected, the electron clouds must be 10,000 bigger, so its size in this model would be:

    D=kd=(10,000)(5)=50,000 cm = 500 m

    So, the size of the electron cloud would be 500 m.

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