Question

How could an alpha particle pass straight through the metal foil and strike the center of the phosphor screen on the other side without scattering at all?

Answer 1

I think you refer to  Rutherford's Gold Foil Experiment alpha particles pass through because of the enormous amount of empty space inside the atom. 


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to have its trajectory affected the alpha particle has to pass "near" the nucleus to interact with the positive charge of the nucleus.
the fact is that internally the gold atoms are basically empty space and the nucleus represents only a small portion of the entire volume. only few alpha particles pass near the nucleus 

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-gio-chealafi- hope this helps you, have a nice rest of the day. ily all!!