How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.

Question

Illustration of a 4s orbital showing nodal surfaces and regions of maximum electron probability.

Accepted Answer

welcome back everyone. We need to identify the diagram that shows the correct number of nodal surfaces and regions of maximum electron probability for a five S orbital. So we want to first make note of the different types of nodal surfaces that we can have. We want to recall that for nodal surfaces, these are regions of zero electron density. So we would have little to no probability of finding electrons. So for our nodal surfaces we have two types for our first type we want to recall, we can have angular notes and for our second type we can have radial notes. So beginning with our prompt, we see that we have the five s orbital where five we should recall tells us our principal quantum number represented by the term N. And we would say that our principal quantum number N is equal to five. Next we have us which we should recognize, tells us our sub shell of our orbital. And because we know that we are given the s sub shell, recall that we can determine our angular momentum quantum number represented by the term L. And say that our angular momentum quantum number is equal to zero since we are in the S orbital. And this would come from our lecture notes which we should interpret and memorize and so calculating our angular notes. We want to recall that our angular nodes are represented by our values for L. And so because we determined that L. Is equal to zero, we would say that our angular node Is also equal to zero. Now figuring out what our radial nodes should look like based on our prompt. We want to recall that our radial notes can be found by taking our principal quantum number N. Subtracted from our angular momentum. Quantum number L Subtracted from the # one. And so calculating our radial notes. We have our principal quantum number of five subtracted from our angular momentum Quantum number which we agreed for the S sub shell is always going to be equal to zero. L equals to zero minus our unit one. And this difference gives us a radial node with a value equal to four. And so we can say that therefore For a five s orbital There are four radio surface for nodal surfaces which all would be our radial notes. So, looking at our answer choices, we can already rule out choices A and B. Since choice A says that we have five nodal surfaces. And choice B says that we have or rather choice choice be here says that we have six nodal services. So let's go ahead and roll these two out. And let's look at C and D. Looking at choices C and D. Choice D says that we have five nodal surfaces. We would definitely disagree with that. We just confirmed that a five S orbital definitely should have four nodal surfaces, meaning that choice C would be the correct diagram with the proper representation of our four nodal surfaces and regions of maximum electron probability marked by the color blue. So I hope everything I reviewed was clear. If you have any questions, please leave them down below, and I'll see everyone in the next practice video.

How many nodal surfaces does a 4s orbital have? Draw a cutaway representation of a 4s orbital showing the nodes and the regions of maximum electron probability.

Verified Solution

Key Concepts

Quantum Numbers

Nodal Surfaces

Electron Probability Density