Question

If the outermost electron in an atom is excited to a very high energy state, its orbit is far beyond that of the other electrons. To a good approximation, we can think of the electron as orbiting a compact core with a charge equal to the charge of a single proton. The outer electron in such a Rydberg atom thus has energy levels corresponding to those of hydrogen.
a. What is the radius of the n=100n=100 state of the Bohr hydrogen atom?
b. Sodium is a common element for such studies. How does the radius you calculated in part a compare to the approximately 0.2 nm0.2 \mathrm{~nm} radius of a typical sodium atom?

Solution

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Answered 2 years ago
Answered 2 years ago
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a)

The radius of the electron orbit in n=100n=100 state is:

r=r1n2=0.531010m1002=0.53μm\begin{align*} r&=r_1n^2\\ &=0.53\cdot 10^{-10}\,\text{m}100^2\\ &=\boxed{0.53\,\mu\text{m}} \end{align*}

b)

The radius from part a) is more then 1000 times bigger then the radius of the sodium atom.

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