Suppose that in an alternate universe, the possible values of l a...

Question

Suppose that in an alternate universe, the possible values of l are the
integer values from 0 to n (instead of 0 to n - 1). Assuming no
other differences between this imaginary universe and ours, how
many orbitals would exist in each level?
a. n = 1
b. n = 2
c. n = 3

Accepted Answer

hey everyone in this example we need to identify which of the n. N. L combinations are possible and which are not possible. So we should first recall that N will represent our energy level. An L. Represents our angular or azimuth? All quantum number. We should recall that L. Are quantum number is defined by zero or any positive integer. That is less. We can say that is less Than N -1. We also want to recall that our angular quantum numbers L correspond to certain sub levels. So beginning with zero we would correspond that to sublevel S one would correspond to sublevel P two would correspond to Sublevel D. And three would correspond to sublevel F. So let's go ahead and begin part A. In part they were given the energy level three. So we can say N is equal to three and we're in the sublevel F. And so we would say that therefore L. Is equal to What f corresponds to as the angular quantum # three. Now, is this going to be possible? Well recalling that our angular quantum number L should be either zero or less than N -1. We would take our energy level for part A which is three and subtract that from one which would give us two. And so our L. Value for part A should either be zero or less than two. So because it's three we would say that therefore not possible. So this would be our answer for part A. Because L should be too Moving on to our 2nd example B. We have four D. As our orbital. This means that we are in the fourth energy level for N. And then our L value because we're in the d sub level Would correspond to two. Now is this possible? What we're going to do is consider taking our end value which would be four subtracting that from one and that would give us three. And so because we did determine that are L. Value is two which is a positive number and is less than three we would say therefore possible because two is less than an equal one. We're sorry and -1. So this would be our answer for part B. Now we can move on to part C which tells us that we're in the first energy level at the sublevel P which corresponds to an L value equal to one. Now is this going to be possible? Well we need to consider our energy level minus one, so that would be one minus one giving us zero. And so therefore we would say that this is not possible Because our l value should equal zero and this is our answer choice for part C. Moving on to Part D. Were given the energy level two and were given the sublevel s which would correspond to the L value equal to zero. So to find our L value, would we consider this possible? We would say our energy level to subtracted from one and that would give us one. So our end value should either be Equal to one or less than one because it's zero, which is less than one. We would say that this is therefore possible And that is due to the fact that zero is less than and -1. So this would be our last and final answer to complete this entire question. Everything boxed in blue represents all of our final answers. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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