**Quantum Numbers in a Hypothetical Universe**In a universe with alternate quantum mechanical rules, the description of atomic structure involves unique quantum numbers defined as follows:1. **Principal Quantum Number (N):** - Values: \( N = 1, 2, 3, \ldots \)2. **Angular Momentum Quantum Number (L):** - Range: \( L \) ranges from 1 to \( N \)3. **Magnetic Quantum Number (M):** - Range: \( M \) ranges from \(-L^2\) to \(+L^2\)**Problem:**Calculate the total number of orbitals available in the first three energy levels under these rules.**Explanation:**- **N = 1:** Only one value for \( L \), and \( L = 1 \). For \( L = 1 \), \( M \) ranges from \(-1\) to \(+1\). Number of orbitals = 3 - **N = 2:** \( L \) can be 1 or 2. - For \( L = 1 \), \( M \) ranges from \(-1\) to \(+1\). Number of orbitals = 3 - For \( L = 2 \), \( M \) ranges from \(-4\) to \(+4\). Number of orbitals = 9 - **N = 3:** \( L \) can be 1, 2, or 3. - For \( L = 1 \), \( M \) ranges from \(-1\) to \(+1\). Number of orbitals = 3 - For \( L = 2 \), \( M \) ranges from \(-4\) to \(+4\). Number of orbitals = 9 - For \( L = 3 \), \( M \) ranges from \(-9\) to \(+9\). Number of orbitals = 19 **Total Orbitals in the First Three Energy Levels:**- \( N = 1 \): 3 orbitals - \( N = 2 \): 12 orbitals - \( N = 3 \): 31 orbitals **Overall Total:

N is the principal quantum number which gives information about the main shell or main energy level…

4. Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms in that universe. These quantum numbers have the following rules. Principle Quantum Number (N) = 1,2,3,... Angular Momentum Quantum Number (L) = range 1 to N Magnetic Quantum Number (M) = -(L²) to +(L²) How many orbitals are there altogether in the first three energy levels?

4. Suppose you live in a different universe where a different set of quantum numbers is required to describe the atoms in that universe. These quantum numbers have the following rules. Principle Quantum Number (N) = 1,2,3,... Angular Momentum Quantum Number (L) = range 1 to N Magnetic Quantum Number (M) = -(L²) to +(L²) How many orbitals are there altogether in the first three energy levels?

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

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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