To solve the problem and fill in the table correctly, we need to determine the values for [tex]\( n \)[/tex], [tex]\( l \)[/tex], [tex]\( m \)[/tex], and [tex]\( m_3 \)[/tex]. Let's analyze and explain the process in detail.
The table summarizes the results:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
n & l & m & m_3 \\
\hline
5 & 1 & 1 & -\frac{1}{2} \\
\hline
\end{tabular}
\][/tex]
Here's an explanation of each value:
1. Value for [tex]\( n \)[/tex]:
- The value of [tex]\( n \)[/tex] is given as 5.
- In many contexts, [tex]\( n \)[/tex] often represents a principal quantum number in quantum mechanics or a term in a sequence.
2. Value for [tex]\( l \)[/tex]:
- The value of [tex]\( l \)[/tex] is given as 1.
- In many scientific contexts, [tex]\( l \)[/tex] represents the azimuthal quantum number or angular momentum quantum number, often an integer indicating the shape of an orbital.
3. Value for [tex]\( m \)[/tex]:
- The value of [tex]\( m \)[/tex] is given as 1.
- In the context of quantum mechanics, [tex]\( m \)[/tex] often represents the magnetic quantum number, which is an integer indicating the orientation of the orbital in space.
4. Value for [tex]\( m_3 \)[/tex]:
- The value of [tex]\( m_3 \)[/tex] is given as [tex]\(-\frac{1}{2}\)[/tex].
- Without further context, [tex]\( m_3 \)[/tex] could be part of a vector or a coordinate in some systems. The value is -0.5.
The table is completed as follows with the values described:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
n & l & m & m_3 \\
\hline
5 & 1 & 1 & -\frac{1}{2} \\
\hline
\end{tabular}
\][/tex]
By understanding the given values and their typical meanings or uses in various contexts, we accurately fill in the table.
