The symbol for an atom containing 20 protons and 22 neutrons is [[1]].

Atomic number (Z) of an element is equal to the number of protons of that element. 

And mass number (A) is defined as the sum of the protons and neutrons of the element.

Now as for the given atom, the atomic number = 20, and thus the element is Calcium ($\mathrm{Ca}$).

The number of neutrons = 22 and the number of protons = 20 , thus mass number of Calcium = 20 +22 = 42.

Hence, the symbol for an atom containing 20 protons and 22 neutrons is $\mathrm{Ca}$.