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First lets see how the lightbulb works.
An electric current, lets say a bunch of electrons pass throught a thin wire made of Wolfram, element 74 of the periodic table.
Here the electrons find a great ressistence to pass throught so they clash with this heavy element's electrons and thus generate lots and lots of heat.
The filament reaches 2000 Cº or so, its electrons now are super excited, and in this bouncing they emmit light.
That's why we call them incandescent, the light comes from heat!
Now in the open when high temperatures are reached we see fire! Fire happens because any combustible material near oxigen and heat gets oxidized!
Now we dont want any reaction of that sort in our bulb, so we put in the most UNreactive type of element we can find, that being a noble gas!
It does not react because its super stable, he has his octet filled, all his electrons are bound to their nucleus and dont interact with other atoms or molecules.
Thus our lightbulb reaches dangerous temperatures without a problem in this inert atmosphere.