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Hydrogen Atom (Worksheet)

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    67426

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    Activity 1

    Calculate the probability that

    1. the electron in a hydrogen atom will be found in a cone with a total opening angle of 10 degrees centered along the z-axis when the atom is in its n=1, \(l = 1\), and \(m_l = 0\) state.
    2. the axis of a diatomic molecule will be found in a cone with a total opening angle of 10 degrees centered along the z-axis when the molecule is in its J = 1, mJ = 0 rotational state.

    Activity 2

    Write the complete hydrogen atom wavefunctions for n = 1, 2, and 3 by combining the appropriate radial function with the appropriate spherical harmonic function. Label these functions with the values for the quantum numbers n, \(l\), and m.

    Activity 3

    Use Mathcad or another computer tool to show the probability densities for the hydrogen atom wavefunctions with values of n = 1, 2, and 3.

    1. To show the distance dependence, plot the radial probability density for some fixed \(\theta\) and \(\varphi\).
    2. To show the \(\theta\) dependence, use a polar plot for some fixed \(\varphi\) and r.
    3. To show the \(\varphi\) dependence, use a polar plot for some fixed \(\theta\) and r.
    4. Choose optimum fixed values or do more than one plot for each.

    Activity 4

    Use Mathcad or another computer tool to construct plots of all the radial wavefunctions with values of n = 1, 2, and 3, their probability densities, and their radial probability densities. Vary the nuclear charge in your plots and examine the effect of nuclear charge on the probability densities. What insights regarding the electronic charge distribution in the hydrogen atom do you get from these plots?

    Hydrogen Atom (Worksheet) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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      1. Exercises