For the table that follows, write which orbital goes with the quantum numbers. Don't worry about

step 1 So now we'll work on problem 62 from chapter 6. In this problem, we're given a table with quantu

For the table that follows, write which orbital goes with...

Key Concepts

Quantum Numbers

Quantum numbers are a set of values used to describe the unique state of an electron within an atom. They include the principal quantum number (n), which indicates the energy level; the azimuthal (or angular momentum) quantum number (l), which defines the shape of the orbital; and the magnetic quantum number (m), which describes the specific orientation of that orbital. Together, these numbers determine the electron’s position and energy, forming the basis for understanding electron configurations in atoms.

Atomic Orbitals

Atomic orbitals are regions around a nucleus where electrons are most likely to be found. They are classified by labels such as s, p, d, and f, which depend on the value of the azimuthal quantum number (l). For instance, an l value of 0 corresponds to an s orbital, l = 1 corresponds to a p orbital, and so on. These orbitals have characteristic shapes and orientations that are critical for understanding chemical bonding and the arrangement of electrons in atoms.

Allowed and Forbidden States

Allowed states are combinations of quantum numbers that satisfy the quantum mechanical rules, such as m being within the range of -l to +l. If the quantum numbers given do not adhere to these rules, the state is considered forbidden. Recognizing these restrictions is important because only allowed states can physically exist in an atom, and any violation of the criteria leads to the designation 'not allowed.'

Transcript

00:01 So now we'll work on problem 62 from chapter 6.

00:08 In this problem, we're given a table with quantum numbers, and it asks us to write which orbital goes with the quantum numbers.

00:17 And we're told not to worry about the x, y, and z subscripts.

00:21 And if the quantum numbers are right, not allowed, we should write not allowed.

00:26 So let's go ahead and put a little table here.

00:29 We have an n value, an l value, and x, ebb sub l value, and then we can write our orbital.

00:40 Let's go ahead and write in the example they give to practice.

00:48 So if we have an n value of two, an l value of one, and an m subl value of negative one, we know that n, the orbital should be, have a two at the beginning because n is equal to two.

01:07 And then the l value tells us.

01:08 That it's a p orbital and m sub al is negative one is a valid quantum number for l is equal to one so it's two p then we're given one zero zero n is equal to one so we put in a one uh l is equal to zero so it's an s orbital and zero is a valid quantum number for m sub l for l is equal to zero so it is 1s orbital.

01:42 Next, we're given 3, negative 3, and 2.

01:48 Now, the 3 here would suggest that we have a 3, the third energy level orbital.

01:57 However, we're given an l value of negative 3.

02:02 And when you have an l value of negative 3, it must be an f orbital.

02:06 However, the 3f orbital does not exist...

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