Question

Find the number of orbitals and maximum electrons respectively present in M-shell?

• A. 4, 8
• B. 9, 18
• C. 16, 32
• D. 1, 2

Hint:

Chemistry Tip: Use the direct formulas for rapid calculations in exams: Total orbitals in a shell $= n^2$, and total maximum electrons in a shell $= 2n^2$.

Answer 1

The Correct Option is B

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

Step 1: Identify the principal quantum number ($n$) 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 $n = 1, 2, 3, 4, ...$ respectively. Therefore, for the M-shell, $n = 3$.

Step 2: Identify the subshells present in the M-shell. For a given principal quantum number $n$, the possible values for the azimuthal quantum number ($l$) range from $0$ to $(n-1)$. For $n=3$, the possible values are $l = 0$ (s-subshell), $l = 1$ (p-subshell), and $l = 2$ (d-subshell).

Step 3: Calculate the total number of orbitals. The number of orbitals in a specific subshell is given by $(2l + 1)$. For $l=0$ (3s), there is $2(0)+1 = 1$ orbital. For $l=1$ (3p), there are $2(1)+1 = 3$ orbitals. For $l=2$ (3d), there are $2(2)+1 = 5$ orbitals. Total orbitals = $1 + 3 + 5 = 9$. Alternatively, the total number of orbitals in an entire shell is simply given by the formula $n^2$. Thus, $3^2 = 9$ 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 $9 \text{ orbitals} \times 2 \text{ electrons/orbital} = 18 \text{ electrons}$.
Alternatively, this can be calculated directly using the standard formula for the maximum electron capacity of a shell, which is $2n^2$.
Substituting $n=3$ gives $2(3)^2 = 2(9) = 18$. The calculated values are 9 orbitals and 18 electrons, perfectly matching option B. $$ \therefore \text{The M-shell has } 9 \text{ orbitals and a maximum of } 18 \text{ electrons.} $$