Give the maximum number of electrons in an atom that can have these quantum numbers: a. n=4 b. n

step 1 All right, guys, zoom, problem 87, chapter 7, giving the maximum number of electrons M that have

Give the maximum number of electrons in an atom that can...

Key Concepts

Electron Capacity in Orbitals and Subshells

The electron capacity concept is based on how many electrons can occupy a given orbital or subshell, taking into account the available quantum numbers and the Pauli exclusion principle. In any orbital defined by a specific set of n, l, and m? values, there can be at most two electrons (one for each spin state). For a complete subshell, the total number of electrons is given by multiplying the number of orbitals (which is 2l + 1) by 2 for the two possible spin states.

Magnetic Quantum Number (m?)

The magnetic quantum number, m?, specifies the orientation of an orbital in space relative to an external magnetic field and ranges from -l to +l in integer steps. Each unique value of m? corresponds to a distinct orbital within a subshell, and when counting electrons, it helps determine how many orbitals share a specific spatial orientation.

Spin Quantum Number (ms)

The spin quantum number, ms, describes the intrinsic spin of an electron, with only two possible values: +1/2 or -1/2. This quantum number is crucial due to the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of all four quantum numbers. It thereby limits the occupancy of each orbital to a maximum of two electrons with opposite spins.

Principal Quantum Number (n)

The principal quantum number, denoted as n, determines the overall size and energy of an orbital. Higher values of n indicate orbitals that are larger and generally have higher energy, and they can accommodate a larger range of angular momentum values. In problems concerning n, one often considers all orbitals within a given energy level regardless of other quantum numbers.

Quantum Numbers

Quantum numbers are a set of numerical values that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), which indicates the energy level and size of the orbital; the angular momentum quantum number (l), which relates to the shape of the orbital; the magnetic quantum number (m?), which indicates the orientation of the orbital in space; and the spin quantum number (ms), which describes the intrinsic angular momentum (spin) of the electron.

Angular Momentum Quantum Number (l)

The angular momentum quantum number, l, defines the orbital shape and determines the subshell in which an electron resides (s, p, d, f, etc.). For a given n, l can take integer values from 0 to n?1. This quantum number is key when analyzing the number of orbitals available in a particular subshell, which in turn affects electron occupancy.

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