Question

The number of orbitals with $\mathrm{n}=5,\mathrm{and}{\mathrm{m}}_1=+2$ is:

Answer 1

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 $"\mathrm{n}"$.

Calculate the number of orbitals:

Given:

$\begin{array}{rcl}\mathrm{quantum}\mathrm{number},\mathrm{n}& =& 5,\\ \mathrm{and}\mathrm{magnetic}\mathrm{quantum}\mathrm{number}{\mathrm{m}}_1& =& +2\end{array}$

To find the number of orbitals, Azimuthal quantum number's expression is used:

$\mathrm{l}=(\mathrm{n}-1)$

putting the value of principle quantum number in above expression:

$\begin{array}{rcl}\mathrm{l}& =& (5-1)\\ & =& 4\end{array}$

Therefore, the possible values of azimuthal quantum number is $\mathrm{l}=0,1,2,3,4.5$

$$\begin{gathered} \mathrm{l}=0\to \mathrm{m}=0 \\ \mathrm{l}=1\to \mathrm{m}=-1,0,+1 \\ \mathrm{l}=2\to \mathrm{m}=-2,-1,0,+1,+2 \\ \mathrm{l}=3\to \mathrm{m}=-3,-2,-1,0,+1,+2,+3 \\ \mathrm{l}=4\to \mathrm{m}=-4,-3,-2,-1,0,+1,+2,+3,+4 \end{gathered}$$

Therefore, the total number of orbitals having quantum number, $\mathrm{n}=5$ and magnetic quantum number, ${\mathrm{m}}_1=+2$ is $3$.