Quantum Mechanical Model Of Atom

Concept: Chemistry (Atomic Structure) - Quantum Numbers and Electron Configuration.

Step 1: Identify the principal quantum number ( ) for the M-shell. Electron shells are designated by letters starting from K. The sequence is K, L, M, N, ..., which corresponds to principal quantum numbers respectively. Therefore, for the M-shell, .

Step 2: Identify the subshells present in the M-shell. For a given principal quantum number , the possible values for the azimuthal quantum number ( ) range from to . For , the possible values are (s-subshell), (p-subshell), and (d-subshell).

Step 3: Calculate the total number of orbitals. The number of orbitals in a specific subshell is given by . For (3s), there is orbital. For (3p), there are orbitals. For (3d), there are orbitals. Total orbitals = . Alternatively, the total number of orbitals in an entire shell is simply given by the formula . Thus, orbitals.

Step 4: State Pauli's Exclusion Principle. According to Pauli's Exclusion Principle, a single atomic orbital can accommodate a maximum of exactly two electrons, and these two electrons must have opposite spins.

Step 5: Calculate the maximum number of electrons. Since we have established that there are exactly 9 orbitals in the M-shell, and each individual orbital can hold a maximum of 2 electrons, we simply multiply these two values to find the total capacity.
The maximum number of electrons is .
Alternatively, this can be calculated directly using the standard formula for the maximum electron capacity of a shell, which is .
Substituting gives . The calculated values are 9 orbitals and 18 electrons, perfectly matching option B. $ $

The azimuthal quantum number defines the shape of the orbital: - → s orbital (spherical) - → p orbital (dumbbell) - → d orbital (cloverleaf) - → f orbital (complex) (a) Principal quantum number determines energy level and size.
(c) Magnetic quantum number determines orientation.
(d) Spin quantum number represents the spin of electron (±½).