In order to answer the question, I'll give you a little summary of the way PHP works.
Let's say I go to example.com/example.html
The server that hosts example.com will receive the request for example.html. It'll look for example.html in its filesystem. Then it'll sent the HTML file to my computer, and my browser will display it.
Now let's say I go to example.com/example.php
The server gets the request for example.php. Let's assume that the server has the PHP software (let's call it php.exe) installed and running, which is needed to use PHP. When it gets ready to serve the file I requested, it looks at the extension on the file. If the file has the .php extension, the server will pass the PHP file to php.exe. Then php.exe will parse the PHP in the file and run all the commands. Then php.exe will sent the results of the commands back to the server. Then the server will send that file to my computer where it is displayed by the browser.
By default, the server will only send a file to php.exe if the file has the .php extension. If the file has the .html extension, is skips php.exe and sends it to my computer directly.
The server doesn't even know whether there are PHP commands inside the .html file--that's php.exe's job. The only thing the server knows is the file's extension. If it has the PHP extension, it'll send it to php.exe regardless of whether or not there are PHP extensions in the file.
HOWEVER...
It's possible to customize a server. You can specify which file extensions you want the server to treat as PHP files. On my server, just for fun, I configured it so that files ending in .z will be sent to php.exe.
There are a couple ways to do this customization. If you're setting up your own server, you can set it up however you want. If you have a website hosted somewhere else, different hosting companies will give you different privileges for customization.
If you're allowed to use .htaccess files in your hosting account, you can add the following line to the main .htaccess file:
addhandler x-httpd-php5 .html
(This assumes the PHP version is PHP5.)
Change ".html" to whatever extension you want, as long as it doesn't conflict with any other special types of extensions. Keep in mind that if you do this for HTML files, this will make every HTML file a little bit slower to serve, because every HTML file will then be sent to php.exe even if it doesn't have PHP code in it. But, this will make PHP code work in HTML files.
If you have a GoDaddy hosting account, you can actually go into your control panel and add extensions to be treated as PHP.
If you want to add this functionality, I suggest that you call your hosting provider and ask if they support this functionality.