"no" is just a simple answer.when sb. ask you sth, you can use ‘no" to answer.But "nope" is a answer with firm emotion.

I agree with Birdfly. Nope says 'no' with a stronger position or stance against doing or a train of thought. Q.Would you like to come to my house for dinner this weekend? A.No, I can't I have too many prior commitments,maybe next weekend, ok? Q. Are you going to visit your father in hospital this week? A. Nope! I really don't care how sick he is, I want nothing to do with him. We don't use 'nope' with our elders, officials, police, teachers or bosses etc. usually. It is usually for friends and family members but I would never use it with my aunt or grandmother.

Nope is used to say no to a friend. There is never a time to use it except for a relaxed situation. If you are talking with a friend in a serious situation you may not want to use it. It is a fun word. Would I suggest using it in an interview to lighten the mood? Nope.