The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (c) In which of the following ways would you modify this sketch if the value of the magnetic quantum number, ml, were to change? (i) It would be drawn larger, (ii) the number of lobes would change, (iii) the lobes of the orbital would point in a different direction, (iv) there would be no change in the sketch.

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Understand the quantum numbers: The magnetic quantum number, m_l, determines the orientation of the orbital in space. It can take values from -l to +l, where l is the azimuthal quantum number.

Identify the effect of m_l: Changing m_l affects the orientation of the orbital but not its size or shape. Therefore, the number of lobes and their size remain unchanged.

Consider the options: (i) It would be drawn larger - this is incorrect as m_l does not affect the size. (ii) The number of lobes would change - this is incorrect as m_l does not affect the number of lobes.

Evaluate the correct option: (iii) The lobes of the orbital would point in a different direction - this is correct as m_l changes the orientation. (iv) There would be no change in the sketch - this is incorrect as m_l affects orientation.

Conclude: The correct modification when m_l changes is that the lobes of the orbital would point in a different direction, corresponding to option (iii).

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주요 개념

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Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. The principal quantum number (n) indicates the energy level, while the magnetic quantum number (ml) specifies the orientation of the orbital in space. Understanding these numbers is crucial for predicting the shape and orientation of atomic orbitals.

Orbital Shapes and Orientation

Atomic orbitals have distinct shapes and orientations based on their quantum numbers. The shape of an orbital is determined by the angular momentum quantum number (l), while the orientation is influenced by the magnetic quantum number (ml). Changes in ml can lead to different orientations of the lobes of the orbital, affecting how they are represented in sketches.

Hydrogen Atom Orbitals

In a hydrogen atom, the orbitals are defined by solutions to the Schrödinger equation, which describe the probability distribution of an electron. For the n = 3 shell, there are multiple orbitals (3s, 3p, 3d) with varying shapes and orientations. Understanding these orbitals helps in visualizing how changes in quantum numbers affect their representation.