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Problem 36 Hard Difficulty

A hydrogen atom is immersed in a magnetic field so that its energy levels split according to the Zeeman effect. Neglecting any effects due to electron spin, how many unique energy levels are available to an electron in the 4$f$ subshell?

Answer

7

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Meghan M.

McMaster University

Video Transcript

In this exercise, we have a hydrogen atom that's emerged on a magnetic field. And we know that due to the zemun effect two states that have originally the same energy when no no magnetic field is present but have different values off the magnetic quantum number and l they are split K. Their energies are split. So the 1st 1 has an energy e plus some absolute. The 2nd 1 has an energy plus, um, other absolute e prime. Okay, eso energy. So states that have the same energy but have different magnetic quantum numbers. Ah, and up having different energies. Ah, So in this exercise, we have an election that's in the four F sub shell of the hydrogen atom. And we want to know how many energy levels are available to this electric once the d Adam is immersed in the magnetic field. Well, in order to calculate that, we need to calculate how many possible values of M L are there. Okay, so the Adam is in the four f ah, in the four ASAP shell. And we know that the F and four f means that l equals three. Okay, It's just another way of saying that the orbital quantum number l equals three. And for a certain l we know that m l varies from minus l to also in our case, this is this range ranges from minus three 23 So it's ministry minus two minus 10 123 So there are three. There are seven different seven different ah values of M l. So 77 values of and l. Okay, so there must be seven different energy energies that are available to the electron that is in the four F sub shell. So seven different energy is available, and this is due to this human effect coming available. Uh, and that's due to the semen effect coming from the presence of the magnetic field, right?

Universidade de Sao Paulo
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Meghan M.

McMaster University