Determine the quantum numbers 𝑛 and ℓ and select all possible va...

Question

Determine the quantum numbers 𝑛 and ℓ and select all possible values for 𝑚ℓ for each subshell of the element.

Accepted Answer

Welcome back everyone in this example we need to identify the sets of values for the principle quantum number, our angular momentum quantum number and then our magnetic quantum number for each orbital in the four D. Sub shell. So we want to recall that the D. Sub shell always contains a total of five orbital's which can hold a maximum Of electrons. So we can say maximum of tell 10 electrons held here. So this is all in response to our D orbital or D. Sub shell. Sorry. And we want to recognize that we have specifically given four D. And so what 40 tells us is that we are at the fourth energy level, recall the energy level is represented by the term N. And so this means that our electron, it's present in this sub shell at the fourth energy level. So now that we have that outlined and we know our value for N. Let's get into what our principal quantum number represents. So principal quantum number we want to recall is represented by the symbol N. And this is referring to the energy level of our orbital and it can only be positive integers starting from one. So right now we can say that our principal quantum number is an equal to the value for as we stated above. Moving on to our next category, we have our angular momentum quantum number. We want to recall that this is represented by our symbol L. And this is going to be a range From zero up to N -1. So we'll use the purple color for N minus one. And so this is going to correspond to each shrub shell. Our angular momentum quantum number refers to. So because we know it can range from zero up to one When we have an L. Value equal to a value of zero. That tells us that we are at our S. Sub shell. When we have an L. Value equal to a value of one. That tells us we are at our P. Sub shell. When we have an L. Value equal to two. That tells us we're at our D. Sub shell. And then when we have an L. Value equal to three that tells us we're in our F sub shell. So moving on to our next category which is our magnetic quantum number, recall that that is represented by the symbol M symbol and it ranges from negative L. Two, positive L. And if we know our L. Value is based on the type of sub shell we have and the prompt gives us 40. So we're given the four D. Sub shell. We're going to say that we have an l. Value equal to two Based on what the prompt gives us. And if we know our l. value is equal to two because we're at the D sub shell we can say L. Is equal to two. And so therefore Isabelle or magnetic quantum number ranges from negative two to positive two. So we have negative one covered. We have zero positive one and positive too. So the last thing we need to recall before we write our final answer is to recall how many orbital's we have in the D sub shell. So recall again as we stayed above the D sub shell consists of five orbital's sorry orbital's. So thus our quantum number sets. Are we going to have our principal quantum number equal to our energy level being for Then next up we have our angular momentum quantum number which we agreed is to for our D sub shell. And then last we have our magnetic quantum number which we stated begins from negative L. Two positive L. So it would be negative two for our first set covering our first orbital in the D sub shell. Moving on to our second orbital in the D sub shell. We again begin with a principal quantum number of four because we are at the fourth energy level. We then go to our angular quantum number which is still going to be the value too because we know that we are in the four D sub shell which corresponds to an L. Value of two. And then lastly we get negative one as our magnetic quantum number, completing our second orbital. Next we have our third orbital quantum number arrangement where we have again the fourth energy level as our principal quantum number. Again we have an L value of two because we are in the D sub shell and then next we have our Magnetic quantum number which ranges to now zero Or which includes zero. And so next we have our and I'll just make some more room here actually so that everything is visible. So next we move on to our fourth orbital in the D sub shell. Again we have our fourth energy level for our principal quantum number. We have an L. Value or angular momentum quantum number equal to two. Since we are in the D sub shell of the fourth energy level. And then we have our magnetic quantum number ranging to now positive one for this set. And then lastly we have our fifth orbital where again we begin at the fourth energy level. We have an angular momentum quantum number of two because we are in the four D sub shell and we know that that corresponds to an L. Value of two. And then lastly we have our last magnetic quantum number ranging up to positive two as our last value here. So we can actually just say two instead of plus two and plus one. So now that we have these sets now this is actually going to be our final answer. To complete this example as our sets of quantum numbers based on the four D sub shell where our electron resides at. So what's highlighted in yellow is our final answer. If you have any questions please leave them down below. And I'll see everyone in the next practice video

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Determine the quantum numbers 𝑛 and ℓ and select all possible values for 𝑚ℓ for each subshell of the element.

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Quantum Numbers: Magnetic Quantum Number practice set