Convergence of certain sequence in a $C^*$ algebra

Question

Let $(A,\mathbb{R},\alpha)$ be a $C^*$-dynamical system. Consider the following sequence of elements in $A$ defined by

$x_n=\sqrt{\frac{n}{\pi}}\int_{\mathbb{R}}\alpha_t(x)e^{-nt^2}dt$.

How to prove that $x_n \rightarrow x$ in norm?