Expected magnitude of a vector of $n$ i.i.d. random variables as $n\to\infty$

Question

Suppose that $X_i$ are i.i.d. real valued random variables with probability distribution $f(x)$ for $i=1,2,3,\ldots$. Let $Y_n=\left(\sum_{i=1}^nX_i^2\right)^{1/2}$. Assuming that $\mathbb{E}\left[Y_n\right]$ converges in probability to some constant $C$ as $n\to \infty$, how would we compute $C$?