Silent is an adjective and silence is a noun. Silent is an atribute of someone or something. "He remained silent." Silence is a state of being "silent" "The silence was unbearable."

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There are some more examples:Suddenly, the silence was broken by a loud explosion. There was an uneasy silence.( here you see the article with the word silence, it shows that it is a noun) All was silent in the house. (adjective -not making or accompanied by any sound.) Sometimes it's better to remain silent.