How do you write the chemical reaction that takes place in a smoke detector?

It is more a physical reaction than a chemical reaction. The americium in the smoke detector is emitting high-speed alpha particles (helium nuclei). The particles hit molecules in the air and knock off electrons to form ions. So, for example, you might say:

O₂ + He(+2) --> O₂(+1) + e(-1) + He(+2)
(Charge is indicated inside the parentheses.)

See How Smoke Detectors Work for complete details on the inner workings of smoke detectors.

Here are some interesting links:

• Inside a Smoke Detector
• How do smoke detectors intercommunicate?
• How Nuclear Radiation Works
• How Nicotine Works