4. Let the angle between vectors $\boldsymbol{a}, \boldsymbol{b}$ be $60^{\circ}$, and $|\boldsymbol{a}|=1$, $|\boldsymbol{a}-2 \boldsymbol{b}|=\sqrt{13}$. Then $\boldsymbol{b}=(\quad)$.
(A) $\sqrt{2}$
(B) $\frac{3}{2}$
(C) $2 \sqrt{2}$
(D) 2
$$
\begin{array}{l}
\text { Given }|\boldsymbol{a}-2 \boldsymbol{b}|=\sqrt{13} \\
\Rightarrow(\boldsymbol{a}-2 \boldsymbol{b})^{2}=13 \\
\Rightarrow|a|^{2}-4|a||\boldsymbol{b}| \cos \theta +4 b^{2}=13 \\
\Rightarrow|\boldsymbol{b}|=2 \text {. }
\end{array}
$$