This is the 10056th most frequent Japanese word.
途端
"途端" means "the moment" or "just as" something happens.
途端 is used immediately following an action (開けた) to indicate that another event (猫が逃げる) occurred instantaneously.
彼がドアを開けた途端に猫が逃げていった。
As soon as he opened the door, the cat ran away.
途端 is used to describe a prompt reaction following a specific event (警報が鳴り出す).
火災警報が鳴り出した途端、みんなが外に逃げ始めた。
The moment the fire alarm started ringing, everyone began escaping outside.
途端 is used here to emphasize the exact timing when a change/event occurred (部屋が静かになる) following an act (話し始める).