Q: According to the Pauli Exclusion Principle, what is the maximum number of electrons that can occupy a single atomic orbital, and why?

2 electrons, because they must have opposite spins. $$\text{Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.}$$

Question 1

According to the Pauli Exclusion Principle, what is the maximum number of electrons that can occupy a single atomic orbital, and why?

Accepted Answer

2 electrons, because they must have opposite spins. 
$$	ext{Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.}$$

Question 2

Which quantum number is directly associated with the electron spin, and what are its possible values?

Accepted Answer

The spin quantum number $$(m_s)$$, with values $$+\frac{1}{2} or$$ $$-\frac{1}{2}.$$

Question 3

If an electron is the first to fill an orbital, what is its typical spin direction according to convention?

Accepted Answer

Upward, $$m_s = +\frac{1}{2}$$

Question 4

Given the electron configuration for a carbon atom ($$1s^2$$ $$2s^2$$ $$2p^2$$), what are the quantum numbers for the highlighted electron in the $$2p$$ orbital with spin up?

Accepted Answer

$$n=2, l=1, m_l=0, m_s=+\frac{1}{2}$$

Question 5

Which of the following best describes the electron spin for an electron that points down in an orbital diagram?

Accepted Answer

$$m_s = -\frac{1}{2}$$

Question 6

A set of $$5d$$ orbitals is being filled. If the highlighted electron is in the third orbital and has spin down, what are the quantum numbers for this electron?

Accepted Answer

$$n=5, l=2, m_l=0, m_s=-\frac{1}{2}$$

Question 7

Which statement about electron spin is correct?

Accepted Answer

Electron spin is a quantum property with only two possible values: $$+\frac{1}{2}$$ and $$-\frac{1}{2}.$$

Question 8

In a $$2p$$ subshell, how many electrons can have $$m_s = +\frac{1}{2}$$?

Accepted Answer

3

Question 9

Which of the following quantum number sets is NOT allowed for an electron in a $$3p$$ orbital?

Accepted Answer

$$n=3, l=1, m_l=2, m_s=+\frac{1}{2}$$

Question 10

A hospital MRI machine uses the concept of electron spin in its imaging technology. Which property of electrons is most directly utilized in this application?

Accepted Answer

The electron's spin quantum number $$m_s$$

Question 11

If two electrons occupy the same orbital, which of the following must be true?

Accepted Answer

They have opposite spin quantum numbers.

Question 12

Which of the following best explains why no two electrons in an atom can have the same set of four quantum numbers?

Accepted Answer

Because of the Pauli Exclusion Principle.

Question 13

A highlighted electron in a $$4f$$ orbital has quantum numbers $$n=4, l=3, m_l=2, m_s=+\frac{1}{2}. $$Which property does $$l=3$$ indicate?

Accepted Answer

The electron is in an $$f$$ orbital.

Question 14

Which of the following is a valid set of quantum numbers for an electron in a $$2s$$ orbital?

Accepted Answer

$$n=2, l=0, m_l=0, m_s=+\frac{1}{2}$$

Question 15

If an electron in a $$3d$$ orbital has $$m_s = -\frac{1}{2}$$, what does this indicate about its spin?

Accepted Answer

The electron has a downward spin.

Electron Spin and the Pauli Exclusion Principle

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