Why does Hamlet not kill the king in act 3?

In act 3, Hamlet does have an opportunity to kill King Claudius while he is praying, but he chooses not to because he believes that killing Claudius while he is in a state of repentance would send Claudius' soul to Heaven, which Hamlet wants to avoid

Hamlet wants Claudius to be punished eternally in Hell for his sins .He also contemplates whether or not his father's spirit is truly the soul of his father or an evil spirit trying to deceive him , so he hesitates to act based solely on the spirit's word

Hamlet's internal conflicts ,philosophical musings and desire to avenge his father through a scheme rather than impulsive action all contribute to his decision against killing Claudius in act 3 ,further complicating his quest for revenge