When you are doing another work by running gmail in background you have to  keep it checking now and then to find out whether you have any new mail.So as a solution to it enabling gmail desktop notification is better idea.
When enabled, a pop-up window will appear on your desktop, so even if you’re
not looking at Gmail you can always know if someone is trying to contact you.
Follow the steps below.

Step 1: Goto the gear icon in your Gmail window at right side and select settings.

Step 2: Search for General tab.

Step 3: Now search for Desktop Notifications option below General Tab.

Step 4: There you can select your preferences like "New notification On , important notification or mail notification Off".

Step 5: save your changes.

Now you will be able to get a desktop notification of your mails as per the preferences enabled by you