From what I know is that while the AIM-120 AMRAAM has a diameter of 180mm, the PL-12 has 203mm. However, while the PL-12 has a range of only 70km (more recent versions possibly have 100), the newest AIM-120D has a range of 180km. So clearly there is something terribly outdated regarding the Chinese BVRAAMs.
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That still doesn't explain your claim that the Chinese will have lesser missiles in the J-20. Plus frankly speaking, it was 7 inch, compare to 8 inch, so it really doesn't matter that much. Do note that J-20 is a bigger aircraft and from what we know, the weapon bay might even be bigger.