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Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by 3 quantum numbers: n, I, and m, n is known as the number. I is known as the number. m, is known as the number. n specifies / specifies m, specifies quantum quantum quantum

Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by 3 quantum numbers: n, I, and m, n is known as the number. I is known as the number. m, is known as the number. n specifies / specifies m, specifies quantum quantum quantum

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Quantum Numbers in the Schrödinger Equation for Hydrogen** The solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: **n**, **l**, and **mₗ**. - **n** is known as the [ ] quantum number. - **l** is known as the [ ] quantum number. - **mₗ** is known as the [ ] quantum number. These quantum numbers specify various properties: - **n** specifies the [ ], specifying: - **A.** The **subshell - orbital shape.** - **B.** The **energy and average distance** from the nucleus. - **C.** The **orbital orientation.** The diagram includes placeholders to fill in the types of quantum numbers and what they specify. It also contains a small image of Erwin Schrödinger, emphasizing his contribution to quantum mechanics.
Transcribed Image Text:**Quantum Numbers in the Schrödinger Equation for Hydrogen** The solution of the Schrödinger wave equation for the hydrogen atom results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: **n**, **l**, and **mₗ**. - **n** is known as the [ ] quantum number. - **l** is known as the [ ] quantum number. - **mₗ** is known as the [ ] quantum number. These quantum numbers specify various properties: - **n** specifies the [ ], specifying: - **A.** The **subshell - orbital shape.** - **B.** The **energy and average distance** from the nucleus. - **C.** The **orbital orientation.** The diagram includes placeholders to fill in the types of quantum numbers and what they specify. It also contains a small image of Erwin Schrödinger, emphasizing his contribution to quantum mechanics.
**Solution of the Schrödinger wave equation for the hydrogen atom** results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: \( n \), \( l \), and \( m_l \). --- ### If the value of \( n = 4 \) - The quantum number \( l \) can have values from \(\boxed{0}\) to \(\boxed{3}\). - The total number of orbitals possible at the \( n = 4 \) energy level is \(\boxed{16}\). --- ### If the value of \( l = 2 \) - The quantum number \( m_l \) can have values from \(\boxed{-2}\) to \(\boxed{2}\). - The total number of orbitals possible at the \( l = 2 \) sublevel is \(\boxed{5}\).
Transcribed Image Text:**Solution of the Schrödinger wave equation for the hydrogen atom** results in a set of functions (orbitals) that describe the behavior of the electron. Each function is characterized by three quantum numbers: \( n \), \( l \), and \( m_l \). --- ### If the value of \( n = 4 \) - The quantum number \( l \) can have values from \(\boxed{0}\) to \(\boxed{3}\). - The total number of orbitals possible at the \( n = 4 \) energy level is \(\boxed{16}\). --- ### If the value of \( l = 2 \) - The quantum number \( m_l \) can have values from \(\boxed{-2}\) to \(\boxed{2}\). - The total number of orbitals possible at the \( l = 2 \) sublevel is \(\boxed{5}\).
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