Let $X \to \mathbb{A}^1_k$ be a smooth morphisms of varieties over a field $k$. Its generic fiber is a smooth morphism $X_\eta \to \eta = \text{Spec }k(t)$. Is it true that we have an injection

$H^2(X_{et},\mathbb{G}_m) \to H^2((X_\eta)_{et},\mathbb{G}_m)$?

Where does it come from and why does this hold?