Answer
The ethyl radical Lewis structure is enclosed.
Work Step by Step
The outer shell electronic configuration of C is $2s^{2}2p^{2}$.
The outer shell electronic configuration of H is $1s^{1}$.
There the total number of valence electrons is $(4\times2)+(1\times5)=13$.
In order to draw electrons we use small black dots. Each dot represents one electron. Two electrons together make a bond.
Firstly we draw two Carbon atoms with 4 dots around them (4 electrons in outer shell) and then we draw five Hydrogen atoms with 1 dot (1 electron in outer shell).
To achieve octet configuration each Carbon atom has to make 4 bonds. One Carbon atom will have 3 bonds with 3 Hydrogen atoms and 1 bond with other Carbon atom. That second Carbon atom will have two bonds with two Hydrogen atoms, 1 bond with "first" Carbon atom and there will be one electron left.
The ethyl radical, $CH_{3}CH_{2}$, Lewis structure is enclosed.
