Added to jQuery in version 1.4, the .delay() method allows us to delay the execution of functions that follow it in the queue. It can be used with the standard effects queue or with a custom queue. Only subsequent events in a queue are delayed; for example this will not delay the no-arguments forms of .show() or .hide() which do not use the effects queue.
Why don't you try the fadeIn() instead of using a show() with delay().
I think what you are trying to do can be done with this.
Here is the jQuery code for fadeIn and FadeOut() which also has inbuilt method for delaying the process.
$(document).ready(function(){
$('element').click(function(){
//effects take place in 3000ms
$('element_to_hide').fadeOut(3000);
$('element_to_show').fadeIn(3000);
});
}