elementary set theory - Order type of a sum ($bigcup$) of sets

A quick question. Is

$$\textrm{ot}(\bigcup\limits_{\gamma <\lambda}\alpha_{\gamma})=\bigcup\limits_{\gamma <\lambda}\textrm{ot}(\alpha_{\gamma})?$$
where $\textrm{ot}$ stands for the order type (and $\lambda$ can be limit ordinal or not).

It seems like a nice property which can be very much false, but I don't know neither how to prove it nor can I find a counterexample.