$S_n^2$ is unbiased for $\sigma^2$, but $S_n$ is biased for $\sigma$

Suppose $\{X_1,X_2,\dots,X_n\}$ are independent and identically distributed random variables with mean $\mu$ and variance $\sigma^2$. Suppose $S_n^2=\frac1{n-1}\sum_{i=1}^n(X_i-\bar X_n)^2$. Then which of the following statements is not true?