Identify the element, and predict its group and period based on the electronic configuration 1s22s22p63s1.

The electronic configuration is $1s^22s^22p^63s^1$.
Total electrons = $2 + 2 + 6 + 1 = 11$.

For a neutral atom, the number of electrons equals the atomic number. An atomic number of 11 corresponds to Sodium (Na).

b) Predict the group and period of the element based on the configuration shown.

The period number is given by the highest principal energy level (n) in the electronic configuration. In $1s^22s^22p^63s^1$, the highest principal energy level is 3 (from $3s^1$).
The period is 3.

The group number for main group elements is determined by the number of valence electrons (electrons in the outermost shell). In this configuration, the outermost shell is the 3rd shell, which contains 1 electron ($3s^1$).
The group is 1.

a) The element is Sodium (Na).

b) The group is 1 and the period is 3.