Step 1: Recall the structure of the modern (long form) periodic table.
The modern periodic table is arranged based on increasing atomic number.
Step 2: Identify the number of periods.
There are 7 horizontal rows called periods.
Step 3: Identify the number of groups.
There are 18 vertical columns called groups.
Step 4: Match with the options.
The correct description is:
\[
\text{seven periods and eighteen groups}
\]
Final Answer:
\[
\boxed{\text{(B)}}
\]