An element with mass number $81$ contains $31.7\%$ more neutrons as compared to protons. Assign the atomic symbol.

Step 1: Number of neutrons in the element

Let the number of protons in the element be $x$.
Number of neutrons in the elements

$=x+31.7\%\text{of}x$
$=x+0.317x$
$=1.317x$

Step 2: Number of protons in the element

According to the question,
$\text{Atomic mass number}=\text{Number of protons}+\text{Number of neutrons}$

Now we are given, atomic mass number of the element is $81$
$\Rightarrow 81=x+1.317x$
$\Rightarrow 2.317x+81$
$\Rightarrow x=\frac{81}{2.317}=35$

Hence, the number of protons in the element is $35$.

Step 3: Atomic Symbol

Since the atomic number of an atom is defined as the number of protons present in its nucleus, the atomic number of the given element is $35$.
Therefore, the atomic symbol of the element is ${}_{81}^{35}\text{Br}$
Final answer: Atomic symbol of element is ${}_{81}^{35}\text{Br}$