静默 is a formal verb that covers two related but distinct situations: falling silent (in a conversation, meeting, or natural setting) and observing a moment of silence as a sign of mourning or respect. The 'mourn in silence' sense is the more culturally specific one — you'll see it in announcements like 静默一分钟 ('observe a minute of silence'). In everyday speech, 沉默 or 安静 are more common for 'become silent'; 静默 leans literary or ceremonial.