The accompanying drawing shows a contour plot for a dyz
orbital. ...

Question

The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?

Accepted Answer

Welcome back everyone in this example we're showing the shape of an F X. Y. Z. Orbital. So it's an F orbital oriented along the X. Y. Z axis. And we need to identify the smallest magnetic quantum number value possible. So because we're given in the prompt magnetic magnetic quantum number to find, we should recall that that's represented by the symbol M. L. And we should recall that what this means is a value that can range and sorry about that. It can range from negative L. Two, positive L. And because we have this in our definition, this tells us that we need to find L first before we can find our values for Ml and to determine the smallest value of Ml to complete this example. So we should recall what Ellis and we should recall that L is going to be our angular momentum quantum number and we should recall that L values or the angular momentum quantum number values range from zero two, Our energy level N -1. So recall that N. is going to be our shell number slash energy level. So according to the prompt, we're dealing with an F orbital. So we say for an F orbital we should recall that an F orbital has the angular momentum quantum number Which is L equals three. So instead of the arrow, let's just say because we have an F orbital, therefore our angular momentum quantum number is equal to three. And this is always true for an F orbital. And we should recall that this would make sense because we should recall that an F orbital lies within the fourth energy level. So we would say that for an F orbital N is equal to four. And because our angular momentum quantum number, L must range from zero to n minus one. We would say four minus one, which would give us our angular momentum quantum number equal to three. And so this definitely we can verify make sense. So next now that we know that our L value is equal to three, we can go back to our ml value which as we recalled range is from negative L two, positive L. And because we know that we can say that therefore our ml values are equal to, we'll start with negative L. So we would say negative three, which would then take us to negative two, then negative one, then we have zero and then going up to positive L. We would now start out with plus one plus two and the ml value of plus three. And so counting all of these values out, we have 1234567 ml values. And because we have some seven ml values, this tells us that we have for f orbital seven orbital's within our F sub level or sub shell. And this definitely makes sense because we should recall that our f orbital can hold a maximum of 14 electrons in its seven orbital's. So our ml values definitely makes sense due to this rationale. And so according to the prompt we want the smallest ml value possible. And according to what we've determined, the smallest value here would be negative three. So we would say are negative three is going to be the smallest ml value possible For our given orbital. And so for our final answer, we would highlight negative three and highlight that it's the smallest ml value possible. So what's highlighted in yellow here is our final answer. I hope that everything that I reviewed was clear. If you have any questions, please leave them down below. This will correspond to choice D in our multiple choice to complete this example as our final answer. So I will see everyone in the next practice video.

The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?

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