child becoming worried and fearful over death

The problem is that what you deem as "solid evidence" is very different from what a fanatic does

Yeah i know to me that's blind faith and if your asking me how to open someones eyes i dont know and as long as they dont impinge on me ie shoving it down my throat why should i try to make them question their own beliefs especially when i want to live in peace,it's when they start trying to convert me they can well lets just say i dont want to be rude!

Being rude can often make your life easier though

Can it i try not to.

I think that you should provide them with a more optimistic look at life and death. Tell the girl that she didn't exist for 13.4 billion years, and it didn't bother her at all, and so there is no need to be afraid of it now. It makes no sense to be afraid of a non-existent circumstance. Also, provide the child with a positive world view, and a guide to living a meaningful life that is void of the superficiality that is ever-present in our society. Help her understand that the universe is neither malevolent nor benevolent. Things happen according to situations and circumstances that have no intent to harm her. Tell her that the fact that life has an ending only gives us more reason to live it meaningfully and value the substantial.

Some children, and even grown people, have a tendency to feel this excessive fear of death. It is likely that she will eventually grow out of it, but take my advise and see if it helps her.

people are going to be afraid of death whether they're religious or not (although, it sure doesn't help when some religious leaders tell people they're probably going to hell when they die). What a child needs to try to understand whether they're religious or not is that death is by no means an end, but a transition. If it's religious, then they're soul will pass on to the afterlife, which can still be scary depending on how strong you are in your theology. If it's not, then their matter and energy will return to the earth, and eventually to the cosmos, recycled in a dynamic process in which matter and energy is never lost, only converted. Of course then you'll have to deal with what happens to the consciousness and the ego when you die, which will be either very easy or very difficult, depending on how perceptive and adept your child is.

Both realities put me at ease when I think about dying. I gotta go with an aphorism from John Dunne who said when we die, the records in the archives of our lives are not erased or destroyed, but translated into a better language.