Problem: Radial probability distributions for the 1s , 2s , and 3s  orbitals of hydrogen. These plots show the probability of finding the electron as a function of distance from the nucleus. As n increases, the most likely distance at which to find the electron (the highest peak) moves farther from the nucleus.How many maxima would you expect to find in the radial probability function for the 4s  orbital of the hydrogen atom?

FREE Expert Solution

From the radial probability distribution plots, we can see that:

  • principal quantum number, n → corresponds to n peaks (or maxima) 
    • 1s has 1 maxima, 2s has 2 maxima, 3s has 3 maxima 

 

View Complete Written Solution
Problem Details


The first graph is for 1s, and shows a sharp peak to about 90% of the Y-axis at around 0.5 angstroms (the most probable distance from the nucleus), before tapering to near-zero by 3 angstroms from the nucleus. The second graph is for 2s, which shows a low peak at around 0.5 angstroms then drops to 0 at 1 angstrom, which is a node.  Then the curve increases with a medium-width hump to a peak about 90% of the Y-axis at around 3 angstroms (the most probable distance from the nucleus), before tapering to near-zero by 8 angstroms. The third graph is for 3s, which shows a low peak at 0.5 angstroms, a node at 1 angstrom, a medium peak at around 2 angstroms, and another node at 4 angstroms.  After that, a very broad hump of maximum probability peaks around 7 angstroms (the most probable distance from the nucleus), before dropping to around 40% probability by 10 angstroms.


Radial probability distributions for the 1s , 2s , and 3s  orbitals of hydrogen. These plots show the probability of finding the electron as a function of distance from the nucleus. As n increases, the most likely distance at which to find the electron (the highest peak) moves farther from the nucleus.


How many maxima would you expect to find in the radial probability function for the 4s  orbital of the hydrogen atom?


Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Wave Function concept. If you need more Wave Function practice, you can also practice Wave Function practice problems.