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Question 31

A certain orbital has no angular nodes and two radial nodes. The orbital is:

Solution

For any orbital, the number of angular nodes equals $$l$$ (the azimuthal quantum number), and the number of radial nodes equals $$n - l - 1$$, where $$n$$ is the principal quantum number.

We are told the orbital has no angular nodes, so $$l = 0$$, meaning it is an $$s$$-orbital. It has two radial nodes, so $$n - 0 - 1 = 2$$, giving $$n = 3$$.

Therefore, the orbital is $$3s$$.

The answer is $$\boxed{3s}$$.

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