It depends on who shoot the plane.

With the spirit of Juche idea, Kim Il Sung (Supreme leader of North Korea) can shoot planes with handgun easily. There is a selection from North Korea textbook:)

>General Kim Il Sung left the cave and saw several of the bombers from US imperialists bombarding the base continuously. The heroic People's Army soldiers kept shooting the American aircrafts but useless.
>
>Frowning angrily , the General saw an American aircraft tried to bomb again, he raised his handgun and aimed at the enemy aircraft. When the enemy is aligned the people army again and came down, the General shot. Shortly, a mass of huge fireball erupted in the sky with falling wreckage. The remaining US pilots were scared and escaped. Soldiers cheered toward the General Kim Il Sung:

>Long live the Great Leader Kim Il Sung!

>Long live the Great General Kim Il Sung!

But for other people, it seems impossible. Major damage of shooting comes from explosive within warhead. In WWII, most of the fighters installed 20mm machine gun or even larger, however, there is many case which the heavily shooted fighters have successfully landed on runways and aircraft carriers. Handgun even cannot kill a man for some times, how can it shot down a plane by most people?