Which Is A Correct Set Of Values Of { M $}$ For One Of The Subshells Of { N=2 $}$?A. { -1, 0, 1$}$B. { -1, -2, 0, 1, 2$}$C. { -1, -2, -3, 0, 1, 2, 3$}$D. { -1, -2, -3, -4, 0, 1, 2, 3, 4$}$

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Understanding the Relationship Between Principal Quantum Number (n) and Azimuthal Quantum Number (l)

In chemistry, the study of atomic structure and electron configuration is crucial for understanding the behavior of elements and their compounds. The principal quantum number (n) and the azimuthal quantum number (l) are two key parameters that describe the energy levels and orbital shapes of electrons in an atom. In this article, we will explore the relationship between n and l, and how it affects the possible values of the magnetic quantum number (m).

The Principal Quantum Number (n)

The principal quantum number (n) is a positive integer that describes the energy level or shell of an electron. It is a measure of the distance of the electron from the nucleus, with higher values of n indicating greater distances. The value of n determines the size of the orbital and the number of electrons that can occupy it.

The Azimuthal Quantum Number (l)

The azimuthal quantum number (l) is a non-negative integer that describes the shape of the orbital. It is a measure of the orbital's angular momentum, with higher values of l indicating greater angular momentum. The value of l determines the orbital's shape and orientation in space.

The Magnetic Quantum Number (m)

The magnetic quantum number (m) is an integer that describes the orientation of the orbital in a magnetic field. It is a measure of the orbital's magnetic moment, with higher values of m indicating greater magnetic moment. The value of m determines the orbital's alignment with the magnetic field.

Relationship Between n, l, and m

The values of n, l, and m are related through the following equations:

  • n = 1, 2, 3, ...
  • l = 0, 1, 2, ..., n-1
  • m = -l, -l+1, ..., 0, ..., l-1, l

Determining the Correct Set of Values for m

Given the value of n = 2, we can determine the possible values of l and m. Since n = 2, the possible values of l are:

  • l = 0, 1

For l = 0, the possible values of m are:

  • m = -0, 0, 0 (since l = 0, m can only be 0)

For l = 1, the possible values of m are:

  • m = -1, 0, 1

Therefore, the correct set of values for m is:

  • m = -1, 0, 1

Conclusion

In conclusion, the correct set of values for m is A. [-1, 0, 1]. This is because the value of n = 2 determines the possible values of l, which in turn determine the possible values of m. The relationship between n, l, and m is a fundamental concept in chemistry that is essential for understanding the behavior of electrons in atoms.

Common Misconceptions

Some students may be tempted to choose option B, C, or D, but these options are incorrect. Option B includes values of m that are not possible for l = 1, while options C and D include values of m that are not possible for any value of l.

Key Takeaways

  • The principal quantum number (n) determines the energy level or shell of an electron.
  • The azimuthal quantum number (l) determines the shape of the orbital.
  • The magnetic quantum number (m) determines the orientation of the orbital in a magnetic field.
  • The values of n, l, and m are related through the equations n = 1, 2, 3, ..., l = 0, 1, 2, ..., n-1, and m = -l, -l+1, ..., 0, ..., l-1, l.
  • The correct set of values for m is A. [-1, 0, 1] for n = 2.
    Frequently Asked Questions (FAQs) About the Relationship Between n, l, and m

In the previous article, we explored the relationship between the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m). In this article, we will answer some frequently asked questions (FAQs) about this topic.

Q: What is the difference between n and l?

A: The principal quantum number (n) determines the energy level or shell of an electron, while the azimuthal quantum number (l) determines the shape of the orbital. In other words, n tells us where the electron is, while l tells us how the electron is arranged.

Q: What is the significance of the value of l?

A: The value of l determines the orbital's angular momentum, which affects the orbital's shape and orientation in space. For example, l = 0 corresponds to an s-orbital, while l = 1 corresponds to a p-orbital.

Q: How do I determine the possible values of m for a given value of l?

A: To determine the possible values of m for a given value of l, you can use the equation m = -l, -l+1, ..., 0, ..., l-1, l. For example, if l = 1, the possible values of m are -1, 0, 1.

Q: What is the relationship between n and the number of electrons in an orbital?

A: The value of n determines the number of electrons that can occupy an orbital. For example, the 1s orbital can hold up to 2 electrons, while the 2s orbital can hold up to 2 electrons.

Q: Can an electron occupy multiple orbitals at the same time?

A: No, an electron cannot occupy multiple orbitals at the same time. Each electron occupies a specific orbital, and the Pauli Exclusion Principle states that no two electrons can have the same set of quantum numbers.

Q: How do I determine the correct set of values for m for a given value of n?

A: To determine the correct set of values for m for a given value of n, you need to determine the possible values of l and then use the equation m = -l, -l+1, ..., 0, ..., l-1, l. For example, if n = 2, the possible values of l are 0 and 1, and the possible values of m are -1, 0, 1 for l = 1.

Q: What is the significance of the value of m?

A: The value of m determines the orientation of the orbital in a magnetic field. Electrons with different values of m will have different magnetic moments, which affects their behavior in a magnetic field.

Q: Can an electron's value of m change in a magnetic field?

A: Yes, an electron's value of m can change in a magnetic field. This is known as Zeeman splitting, and it occurs when an electron's orbital is aligned with the magnetic field.

Q: How do I determine the correct set of values for m for a given value of l?

A: To determine the correct set of values for m for a given value of l, you can use the equation m = -l, -l+1, ..., 0, ..., l-1, l. For example, if l = 1, the possible values of m are -1, 0, 1.

Q: What is the relationship between n, l, and the energy of an electron?

A: The energy of an electron is determined by the values of n and l. Electrons in higher energy levels (n > 1) have higher energies than electrons in lower energy levels (n = 1).

Q: Can an electron's energy change in a magnetic field?

A: Yes, an electron's energy can change in a magnetic field. This is known as Zeeman splitting, and it occurs when an electron's orbital is aligned with the magnetic field.

Conclusion

In conclusion, the relationship between n, l, and m is a fundamental concept in chemistry that is essential for understanding the behavior of electrons in atoms. By understanding the possible values of m for a given value of l, you can determine the correct set of values for m and understand the significance of the value of m.