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