QuestionJuly 1, 2025

How many maxima would you expect to find in the radial probability function for the 6s orbital of the hydrogen atom? Express the number of maxima as an integer.

How many maxima would you expect to find in the radial probability function for the 6s orbital of the hydrogen atom? Express the number of maxima as an integer.
How many maxima would you expect to find in the radial probability function for the 6s orbital of the hydrogen atom?
Express the number of maxima as an integer.

Solution
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Answer

5 Explanation 1. Identify the radial probability function The radial probability function for an s orbital is given by P(r) = r^2 |R_{nl}(r)|^2, where R_{nl}(r) is the radial wavefunction. 2. Determine the number of maxima For a hydrogen atom, the radial wavefunction R_{nl}(r) for an s orbital has (n-1) nodes. Each node corresponds to a maximum in the radial probability function. For the 6s orbital, n=6, so there are 5 nodes.

Explanation

1. Identify the radial probability function<br /> The radial probability function for an $s$ orbital is given by $P(r) = r^2 |R_{nl}(r)|^2$, where $R_{nl}(r)$ is the radial wavefunction.<br /><br />2. Determine the number of maxima<br /> For a hydrogen atom, the radial wavefunction $R_{nl}(r)$ for an $s$ orbital has $(n-1)$ nodes. Each node corresponds to a maximum in the radial probability function. For the 6s orbital, $n=6$, so there are $5$ nodes.
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