Send email notification when user role changes

function user_role_update( $user_id, $new_role ) {
        $site_url = get_bloginfo('wpurl');
        $user_info = get_userdata( $user_id );
        $to = $user_info->user_email;
        $subject = "Role changed: ".$site_url."";
        $message = "Hello " .$user_info->display_name . " your role has changed on ".$site_url.", congratulations you are now an " . $new_role;
        wp_mail($to, $subject, $message);
}
add_action( 'set_user_role', 'user_role_update', 10, 2);