Question

The number of orbitals associated with quantum number $\mathrm{n}=5$, $\mathrm{ms}=+\frac{1}{2}$ is :

• A. $11$
• B. $15$
• C. $25$
• D. $50$

Answer 1

The correct option is C

$25$

The explanation for the correct option:

(C): $25$

Principle Quantum Number:

• The fundamental quantum number, or $"\mathrm{n}"$ has the values $1,2,3,\mathrm{and}\mathrm{so}\mathrm{on}$.
• The primary quantum number reveals the orbital's size and energy.
• One atom's shell is present in each of the orbitals of the number $"\mathrm{n}"$.

Number of orbitals associated with quantum number, $\mathrm{n}=5$ and $\mathrm{ms}=+\frac{1}{2}$:

Given:

• $\mathrm{n}=5$ and magnetic spin number, $\mathrm{ms}=+\frac{1}{2}$
• To find the number of subshells that are involved in it, Azimuthal quantum number's expression is used:
• $\mathrm{l}=\left(\mathrm{n}-1\right)$
• putting the value value of principle quantum number in above expression:
• $\begin{array}{rcl}\mathrm{l}& =& (5-1)\\ & =& 4\end{array}$
• Hence the possible sub-shells for $\mathrm{n}=5$ are: $5\mathrm{s},5\mathrm{p},5\mathrm{d},5\mathrm{f}\mathrm{and}5\mathrm{g}$.
• The number of orbitals each would have, be $1,3,5,7,9$ respectively and the total sum of these numbers is$25$.

Final Answer: Therefore, Option C is the correct option.