The fourth quantum number, m_{s}, determines the spin of an electron within an atomic orbital.

Whereas the first 3 quantum numbers describe the atomic orbital where you find the electron, the final quantum number, m_{s}, describes spin the electron possesses.

Concept #1: Spin Quantum Number Part 1

The **Pauli Exclusion Principle** implies that two electrons in the same atomic orbital cannot spin in the same direction so as to avoid having the same four quantum numbers.

Concept #2: Spin Quantum Number Part 2

Example #1: State the electron configuration of boron and list the four quantum numbers of the 1** ^{st}** and the 5

What are the four quantum numbers for each of the two electrons in a 4s orbital?For first electron:

What are the four quantum numbers for each of the two electrons in a 4s orbital?For second electron:

Why is electron spin important when writing electron configurations?

Electron spin. The electron
behaves as if it were spinning about an axis,
thereby generating a magnetic field whose
direction depends on the direction of spin.
The two directions for the magnetic field
correspond to the two possible values for the
spin quantum number, ms.From this figure, why are there only
two possible values for the spin
quantum number?

Imagine a universe in which the value of ms can be +1/2, 0, and -1/2. Assuming that all the other quantum numbers can take only the values possible in our world and that the Pauli exclusion principle applies, give the following.the new electronic configuration of neon

Imagine a universe in which the value of ms can be +1/2, 0, and -1/2. Assuming that all the other quantum numbers can take only the values possible in our world and that the Pauli exclusion principle applies, give the following.the atomic number of the element with a completed n = 2 shell

Imagine a universe in which the value of ms can be +1/2, 0, and -1/2. Assuming that all the other quantum numbers can take only the values possible in our world and that the Pauli exclusion principle applies, give the following.the number of unpaired electrons in fluorine

You may want to reference (Pages 236 - 236) Section 6.7 while completing this problem.An experiment called the Stern–Gerlach experiment helped
establish the existence of electron spin. In this experiment,
a beam of silver atoms is passed through a magnetic field,
which deflects half of the silver atoms in one direction and
half in the opposite direction. The separation between the
two beams increases as the strength of the magnetic field
increases.

A certain orbital of the hydrogen atom has n = 4 and l = 2.What are the possible values of ms for the orbital?

A hydrogen atom orbital has n = 5 and ml = -2 .What are the possible values of ms for the orbital?

In the experiment shown schematically below , a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams.What do you think would happen if the strength of the magnet were increased?

In the experiment shown schematically below , a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams.What do you think would happen if the beam of hydrogen atoms were replaced with a beam of helium atoms?

In the experiment shown schematically below , a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams.The relevant experiment was first performed by Otto Stern and Walter Gerlach in 1921. They used a beam of Ag atoms in the experiment. By considering the electron configuration of a silver atom, explain why the single beam splits into two beams.

In the experiment shown schematically below , a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams.Why?

Suppose that the spin quantum number, ms, could have three allowed values instead of two.What would be the number of elements in the first row of the periodic table?

Suppose that the spin quantum number, ms, could have three allowed values instead of two.What would be the number of elements in the second row of the periodic table?

Suppose that the spin quantum number, ms, could have three allowed values instead of two.What would be the number of elements in the third row of the periodic table?

Suppose that the spin quantum number, ms, could have three allowed values instead of two.What would be the number of elements in the fourth row of the periodic table?

Which of the following is a possible set of quantum numbers for a 3d electron?a) n=4, l=3, m l=2, ms=-1/2 b) n=3, l=2, m l=0, ms=-1/2c) n=3, l=1, m l=1, ms=+1/2d) n=3, l=3, m l=2, ms=+1/2e) n=3, l=0, m l=0, ms=+1/2

How many electrons can have the following quantum numbersa) n=3, l=1, ms=1/2 b) n=4, m l = -1

What is the smallest acceptable value for the missing quantum number?n = ?, ℓ = 2, mℓ = 0, ms = +1/2A) 4B) 3C) 1D) 5E) 2

Which of the following set is an acceptable set of quantum numbers? a. n = 0, l = 0, m l = 0, m s = +1/2b. n = 2, l = 1, m l = 2, m s = −1/2c. n = 2, l = 0, m l = 0, m s = 1d. n = 1, l = 1, m l = 0, m s = −1/2e. n = 3, l = 1, m l = −1, m s = −1/2

Which set of quantum numbers is not possible?a) n = 2, l = 1, m l, = +1, m s = –1/2b) n = 3, l = 2, m l = +1, m s = +1/2c) n = 4, l = 4, m l = –1, m s = +1/2d) n = 5, l = 2, m l = 2, m s = –1/2

For an electron that has quantum numbers n = 3 and m l = 2, which of the following is true?A) it must have the quantum number m s = + 1/2B) it must have the quantum number l = 1C) it may have the quantum numbers, l = 0, 1, 2D) it must have the quantum number l = 2E) none of these answers apply to this electron

Which of the following represents an impossible set of quantum numbers for an electron in an atom?a. 2, 1, -1, -1/2 b. 1, 0, 0, +1/2c. 3, 3, 3, +1/2 d. 5, 4, -3, +1/2 e. 5, 4, -3, -1/2

Which one of the following represents a 2p electron in an atom?a. 2, 1, -1, +1/2b. 2, 1, 0, 0c. 2, 2, 0, -1/2d. 2, 0, 1, -1/2 e. 2, 0, 2, +1/2

Which of the following set of quantum numbers (ordered n, ℓ, m ℓ, ms) are possible for an electron in an atom? Check all that apply.a. 5, 3, 0, 1/2b. 2, 1, 0, 1/2c. 3, 1, 0, -1/2d. 2, 1, 0, 1e. 2, 1, -2, 1/2f. 3, 4, 0, 1/2g. 5, 3, 4, 1/2h. -1, 0, 0, -1/2

Part AWhat is the only possible value of ml for an electron in an s orbital?Express your answer numerically.Part BWhat are the possible values of m l for an electron in a d orbital?Express your answer numerically with sequential values separated by commas.Part CWhich of the following set of quantum numbers (ordered n, l, m l, ms) are possible for an electron in an atom?

Which one of the following statements is false?a. If an electron quantum number n=2, it may be a p sublevel.b. If an electron has ℓ=1, it must be in a p sublevel.c. Two electrons in the same atom may have quantum numbers, n , l , mℓ , ms of 2,1,-1,½, and 2,-1,- 1,½.d. Two electrons in the same atom may not have quantum numbers of 2,1,-1,-½ and 2,1,-1,-½.e. If an electron has n=1, it must be in an s orbital

Which of the following set of quantum numbers (ordered n,l,ml,ms) are possible for an electron in an atom? Check all that apply.a. 3, 4, 0, 1/2b. 3, 2, 0, -1/2c. 3, 2, 2, -1/2d. 3, 1, 0, -1/2e. -3, 2, 2, -1/2f. 4, 3, 4, -1/2g. 2, 1, 0, 1h. 2, 1, -2, 1/2

Which of the following sets of the four quantum numbers n, l, m l, and ms decribes one of the outermost electrons in a ground-state barium atom?a) 6, 1, 1, ½b) 6, 0, 1, -½c) 6, 0, 0, -½d) 6, 1, 0, ½e) 6, 2, 1, -½

Identify which sets of quantum numbers are valid for an electron. Each set is ordered(n,l,ml,ms). Select all that apply.3,0, 0,1/20,2,1,-1/23,2,2,1/22,1,0,1/24,3,5,-1/23,1,-1,1/22,2,-1,1/24,3,1,-1/22,2,1,-1/21,-1,-1,-1/23,3,1,1/23,-2,-1,0

Which of the following is a possible set of quantum numbers?

Which set of quantum numbers is correct and consistent with n = 4?(A) l = 3 m l = -3 ms = +1/2(B) l = 4 m l = +2 ms = -1/2(C) l = 2 m l = +3 ms = +1/2(D) l = 3 m l = -3 ms = +1

How many electrons can have the following quantum sets? a. In the 7 th shell of an atom (n = 7)b. n = 5, ℓ = 2c. n = 6, ℓ = 3, m ℓ = -2d. n = 4, ℓ = 2, m ℓ = 0 , m s = -1/2e. n = 4, m ℓ = -1f. n = 5, m ℓ = 0 , m s = 1/2g. n = 9, ℓ = 4, m s = -1/2h. n = 2, m s = 1/2

Each of the following sets of quantum numbers gives information on a specific orbital. Find the error in each. a) n = 4, l = 0 , m l = 1, m s = -1/2b) n = 5, l = 2 , m l = - 1, m s = 1c) n = 7, l = 7, m l = - 5, m s = -1/2d) n = 22, l = 5, m l = - 6, m s = 1/2

Fluorine can gain an electron to become fluoride (F−). What is the quantum number (following the numbering conventions) that describes the electron that was gained by fluorine.(a) n = 2, ℓ = 0, m ℓ = 1, ms = -1⁄2(b) n = 2, ℓ = 1, m ℓ = 0, ms = -1⁄2(c) n = 3, ℓ = 1, m ℓ = 1, ms = +1⁄2(d) n = 2, ℓ = 1, m ℓ = 1, ms = -1⁄2(e) n = 2, ℓ = 1, m ℓ = -1, ms = -1⁄2

Which of the following represents a set of quantum number for valence electron of Chlorine?A. (3,1,0,-1)B. (3, 2, 0, -1/2)C. (3,0,2, 1/2)D. (3,1,-1, -1/2)E. (3,1,0,0)

How many of the following statements are false?I. The principal quantum number n is related to the size of an orbital.II. s, p, d, f represent orbitals with different azimuthal quantum numbers.III. The magnetic quantum number can have values of +½ or -½.IV. The spin quantum number is related to the orientation of an orbital.V. The electron density at a point is proportional to Ψ 2 at that point.A. 0B. 1C. 2D. 3E. 4

Which of the following is not a permitted combination of quantum numbers?1. n = 4, ℓ = 2, mℓ = 1, m s = 1/22. n = 3, ℓ = 0, mℓ = 0, m s = 1/23. n = 4, ℓ = 3, mℓ = 3, m s = − 1/24. n = 2, ℓ = 1, mℓ = −2, m s = 1/25. n = 3, ℓ = 0, mℓ = 0, m s = − 1/2

List all the quantum numbers for each of the 9 electrons in fluorine. n l ml ms.

What are the allowed values for each of the four quantum numbers: n, l, m l, and m s?

Which of the following sets of quantum numbers are not allowed? For each incorrect set, state why it is incorrect.a. n = 3, ℓ = 3, mℓ = 0, ms = -1/2b. n = 4, ℓ = 3, mℓ = 2, ms = -1/2c. n = 4, ℓ = 1, mℓ = 1, ms = +1/2d. n = 2, ℓ = 1, mℓ = -1, ms = -1e. n = 5, ℓ = -4, mℓ = 2, ms = +1/2f. n = 3, ℓ = 1, mℓ = 2, ms = -1/2

In the ground state of mercury, Hg, how many electrons have spin “up” (ms = +1/2)?

Give a combination of four quantum numbers that could be assigned to an electron occupying a 5p orbital.

You may want to reference(Pages 349 - 350) Section 8.4 while completing this problem.Which set of four quantum numbers corresponds to an electron in a
4p orbital?

What are the possible quantum numbers for the last electron in zinc?n = ___________l = ___________ml = __________ms = ___________