Using widget logic I want to show only a widget on the archive page if there are no posts

I have a custom post type with it’s own taxonomy and I need to display a widget when on a category archive that is ONLY displayed when there are no posts. Currently I’m using this:

 is_tax( 'genre' )    

in the widget logic so that it only displays for that taxonomy but it is being displayed all the time. When there is a post for that category the widget should disappear. Any suggestions?

The have_posts() function checks if the ‘main query’ returned any posts. is_tax can check if a certain taxonomy archive page is being shown.

In this case, the solution (taken from the comments):

if( is_tax( 'genre' ) && !have_posts() ){
 //Display widget
}