Answer
Please see the work below.
Work Step by Step
We know that the first period of the periodic table has the following allowed quantum number.
$n=1,l=1$, $m_l=0,+1,-1,m_s=+\frac{1}{2},-\frac{1}{2}$
As there are six different combinations hence there would be six elements in the first period of the periodic table.
